Number of the day: 50632831854

Carl Ludwig Siegel was born on this day 124 years ago.

Properties of the number 50632831854:

50632831854 = 2 × 3² × 11 × 113 × 523 × 4327 is composite and not squarefree.
50632831854 has 6 distinct prime factors, 96 divisors, 55 antidivisors and 15174915840 totatives.
50632831854 has a triangular digit sum 45 in base 10.
50632831854 is the difference of 2 positive pentagonal numbers in 5 ways.
50632831854 = 257² + 1678² + 225011² is the sum of 3 positive squares.
50632831854² = 6721172370² + 50184753696² is the sum of 2 positive squares in 1 way.
50632831854² is the sum of 3 positive squares.
50632831854 is a proper divisor of 463¹⁷³⁰⁴ - 1.
50632831854 = '506' + '32831854' is the concatenation of 2 sphenic numbers.

Number of the day: 9970365787

Properties of the number 9970365787:

9970365787 is a cyclic number.
9970365787 = 83 × 120124889 is semiprime and squarefree.
9970365787 has 2 distinct prime factors, 4 divisors, 63 antidivisors and 9850240816 totatives.
9970365787 has a prime digit sum 61 in base 10.
Reversing the decimal digits of 9970365787 results in an emirpimes.
9970365787 = 4985182894² - 4985182893² = 60062486² - 60062403² is the difference of 2 nonnegative squares in 2 ways.
9970365787 is the sum of 2 positive triangular numbers.
9970365787 is the difference of 2 positive pentagonal numbers in 2 ways.
9970365787 = 725² + 2451² + 99819² is the sum of 3 positive squares.
9970365787² = 1975208187² + 9772755320² is the sum of 2 positive squares in 1 way.
9970365787² is the sum of 3 positive squares.
9970365787 is a proper divisor of 17^4493723 - 1.
9970365787 = '99703' + '65787' is the concatenation of 2 semiprime numbers.
9970365787 is an emirpimes in (at least) the following bases: 5, 6, 10, 14, 20, 22, 25, 26, 29, 30, 32, 35, 38, 41, 50, 51, 54, 55, 59, 61, 62, 66, 68, 73, 77, 81, 83, 85, 86, 88, 89, 90, 92, 93, 94, 95, 96, and 99.

Number of the day: 75991

Thomas Joannes Stieltjes was born on this day 164 years ago.

Properties of the number 75991:

75991 is a cyclic number.
75989 and 75991 form a twin prime pair.
75991 has 19 antidivisors and 75990 totatives.
75991 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 75991 results in a semiprime.
75991 = 37996² - 37995² is the difference of 2 nonnegative squares in 1 way.
75991 is the sum of 2 positive triangular numbers.
75991 is the difference of 2 positive pentagonal numbers in 1 way.
75991 is not the sum of 3 positive squares.
75991² is the sum of 3 positive squares.
75991 is a proper divisor of 1531⁴⁴⁷ - 1.
75991 is an emirp in (at least) the following bases: 3, 5, 9, 11, 14, 15, 16, 20, 23, 28, 29, 34, 35, 39, 42, 49, 51, 57, 59, 63, 65, 75, 77, 79, 83, 91, 93, and 99.
75991 in base 49 = VVf and consists of only the digits 'V' and 'f'.

The number 75991 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A096510: a(n) is the smallest number x such that the number of prime powers (including primes, excluding 1), in the neighborhood of x with radius ceiling(log(x)), equals n.
A096518: Solutions to A096509[x]=7; number of prime-powers [including primes] in the neighborhood of x with Ceiling[Log[x]] radius equals 7.
A106301: Primes that do not divide any term of the Lucas 5-step sequence A074048.
A135843: Prime numbers p of the form 10k+1 for which the pentanacci quintic polynomial x^5-x^4-x^3-x^2-x-1 modulus p is factorizable into five binomials.

Number of the day: 2692

John von Neumann was born on this day 117 years ago.

Properties of the number 2692:

2692 is the 714^th totient number.
2692 = 2² × 673 is the 2300^th composite number and is not squarefree.
2692 has 2 distinct prime factors, 6 divisors, 9 antidivisors and 1344 totatives.
2692 has a prime digit sum 19 in base 10.
2692 has sum of divisors equal to 4718 which is a sphenic number.
Reversing the decimal digits of 2692 results in a semiprime.
2692 = 674² - 672² is the difference of 2 nonnegative squares in 1 way.
2692 is the sum of 2 positive triangular numbers.
2692 is the difference of 2 positive pentagonal numbers in 1 way.
2692 = 24² + 46² is the sum of 2 positive squares in 1 way.
2692 = 8² + 18² + 48² is the sum of 3 positive squares.
2692² = 1540² + 2208² is the sum of 2 positive squares in 1 way.
2692² is the sum of 3 positive squares.
2692 is a proper divisor of 1601³ - 1.
2692 = '269' + '2' is the concatenation of 2 prime numbers.
2692 is palindromic in (at least) the following bases: 3, 24, 39, -28, and -69.
2692 in base 24 = 4g4 and consists of only the digits '4' and 'g'.
2692 in base 36 = 22s and consists of only the digits '2' and 's'.
2692 in base 38 = 1WW and consists of only the digits '1' and 'W'.
2692 in base 39 = 1U1 and consists of only the digits '1' and 'U'.
2692 in base 51 = 11e and consists of only the digits '1' and 'e'.

The number 2692 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A008137: Coordination sequence T1 for Zeolite Code LTA and RHO.
A018846: Strobogrammatic numbers: numbers that are the same upside down (using calculator-style numerals).
A133524: Sum of squares of four consecutive primes.
A179186: Numbers n such that phi(n) = phi(n+4), with Euler's totient function phi=A000010.
A216451: Numbers which are simultaneously of the form x^2+y^2, x^2+2y^2, x^2+3y^2, x^2+7y^2, all with x>0, y>0.
A224133: T(n,k)=Number of nXk 0..1 arrays with rows nondecreasing and antidiagonals unimodal
A238779: Number of palindromic partitions of n with greatest part of multiplicity 2.
A269606: T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by one or less.
A281400: T(n,k)=Number of nXk 0..1 arrays with no element equal to more than two of its horizontal, diagonal or antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
A327244: Number T(n,k) of colored compositions of n using all colors of a k-set such that all parts have different color patterns and the patterns for parts i are sorted and have i colors in (weakly) increasing order; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

Number of the day: 941608

Johannes Kepler was born on this day 449 years ago.

Johannes Kepler was born on this day 449 years ago.

Jacob Bernoulli was born on this day 366 years ago.

Properties of the number 941608:

941608 = 2³ × 117701 is the 867296^th composite number and is not squarefree.
941608 has 2 distinct prime factors, 8 divisors, 29 antidivisors and 470800 totatives.
941608 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 941608 results in a semiprime.
941608 = 58³ + 72³ + 72³ is the sum of 3 positive cubes in 1 way.
941608 = 235403² - 235401² = 117703² - 117699² is the difference of 2 nonnegative squares in 2 ways.
941608 is the difference of 2 positive pentagonal numbers in 2 ways.
941608 = 522² + 818² is the sum of 2 positive squares in 1 way.
941608 = 64² + 66² + 966² is the sum of 3 positive squares.
941608² = 396640² + 853992² is the sum of 2 positive squares in 1 way.
941608² is the sum of 3 positive squares.
941608 is a proper divisor of 1277¹⁰⁷⁰ - 1.

Number of the day: 43460

Charles Babbage was born on this day 229 years ago.

John Horton Conway was born on this day 83 years ago.

Properties of the number 43460:

43460 = 2² × 5 × 41 × 53 is the 38928^th composite number and is not squarefree.
43460 has 4 distinct prime factors, 24 divisors, 15 antidivisors and 16640 totatives.
43460 has an emirp digit sum 17 in base 10.
43460 = (24 × 25)/2 + … + (64 × 65)/2 = (11 × 12)/2 + … + (63 × 64)/2 is the sum of at least 2 consecutive triangular numbers in 2 ways.
43460 = 10866² - 10864² = 2178² - 2168² = 306² - 224² = 258² - 152² is the difference of 2 nonnegative squares in 4 ways.
43460 is the difference of 2 positive pentagonal numbers in 4 ways.
43460 = 136² + 158² = 32² + 206² = 98² + 184² = 14² + 208² is the sum of 2 positive squares in 4 ways.
43460 = 20² + 38² + 204² is the sum of 3 positive squares.
43460² = 26076² + 34768² = 15744² + 40508² = 3772² + 43296² = 24252² + 36064² = 17808² + 39644² = 5824² + 43068² = 28196² + 33072² = 13184² + 41412² = 6468² + 42976² = 30500² + 30960² = 9540² + 42400² = 14300² + 41040² = 22960² + 36900² is the sum of 2 positive squares in 13 ways.
43460² is the sum of 3 positive squares.
43460 is a proper divisor of 83⁴ - 1.
43460 is palindromic in (at least) the following bases: 71, and 97.
43460 in base 19 = 6677 and consists of only the digits '6' and '7'.
43460 in base 23 = 3d3d and consists of only the digits '3' and 'd'.

The number 43460 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A015226: Even hexagonal pyramidal numbers.
A063490: a(n) = (2*n - 1)*(7*n^2 - 7*n + 6)/6.
A111302: Define a(1)=1. Thereafter a(n) is the smallest positive integer with the property that a(n)^2 cannot be created by summing the squares of at most n values chosen among the previous terms (with repeats allowed).

Number of the day: 216093

Properties of the number 216093:

216093 = 3 × 72031 is semiprime and squarefree.
216093 has 2 distinct prime factors, 4 divisors, 23 antidivisors and 144060 totatives.
216093 has a semiprime digit sum 21 in base 10.
216093 has a Fibonacci digit sum 21 in base 10.
216093 has a triangular digit sum 21 in base 10.
216093 = 108047² - 108046² = 36017² - 36014² is the difference of 2 nonnegative squares in 2 ways.
216093 is the difference of 2 positive pentagonal numbers in 1 way.
216093 = 11² + 26² + 464² is the sum of 3 positive squares.
216093² is the sum of 3 positive squares.
216093 is a proper divisor of 907³⁴³ - 1.
216093 is an emirpimes in (at least) the following bases: 2, 6, 15, 21, 48, 50, 54, 57, 58, 65, 69, 72, 78, 83, 89, 92, 96, 99, and 100.

Number of the day: 137206

Properties of the number 137206:

137206 = 2 × 31 × 2213 is a sphenic number and squarefree.
137206 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 66360 totatives.
137206 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 137206 results in a sphenic number.
137206 is the sum of 2 positive triangular numbers.
137206 is the difference of 2 positive pentagonal numbers in 4 ways.
137206 = 26² + 69² + 363² is the sum of 3 positive squares.
137206² = 11656² + 136710² is the sum of 2 positive squares in 1 way.
137206² is the sum of 3 positive squares.
137206 is a proper divisor of 1093⁷⁰ - 1.
137206 is palindromic in (at least) base 82.

Number of the day: 6787

Srinivasa Ramanujan was born on this day 133 years ago.

Properties of the number 6787:

6787 = 11 × 617 is semiprime and squarefree.
6787 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 6160 totatives.
6787 has a triangular digit sum 28 in base 10.
6787 has an oblong digit product 2352 in base 10.
6787 = 3394² - 3393² = 314² - 303² is the difference of 2 nonnegative squares in 2 ways.
6787 is the sum of 2 positive triangular numbers.
6787 is the difference of 2 positive pentagonal numbers in 2 ways.
6787 = 1² + 15² + 81² is the sum of 3 positive squares.
6787² = 1155² + 6688² is the sum of 2 positive squares in 1 way.
6787² is the sum of 3 positive squares.
6787 is a proper divisor of 1409¹¹ - 1.
6787 is an emirpimes in (at least) the following bases: 2, 3, 14, 18, 23, 24, 25, 34, 39, 41, 44, 47, 52, 55, 57, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 81, 89, 91, 92, 94, 95, 96, 98, 99, and 100.
6787 is palindromic in (at least) the following bases: 30, 78, -27, -53, -59, and -87.
6787 in base 26 = a11 and consists of only the digits '1' and 'a'.
6787 in base 30 = 7g7 and consists of only the digits '7' and 'g'.
6787 in base 47 = 33J and consists of only the digits '3' and 'J'.
6787 in base 58 = 211 and consists of only the digits '1' and '2'.

The number 6787 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005674: a(n) = 2^(n-1) + 2^[ n/2 ] + 2^[ (n-1)/2 ] - F(n+3).
A062020: Let P(n) = { 2,3,5,7,...,p(n) } where p(n) is n-th prime; then a(1) =0 and a(n) = Sum [mod{p(i) - p(j)}], for all i and j from 1 to n.
A072481: a(n) = Sum_{k=1..n} Sum_{d=1..k} (k mod d).
A080855: a(n) = (9*n^2 - 3*n + 2)/2.
A082395: Number of shifted Young tableaux with height <= 3.
A107632: Subsequence of A107629. Consider a Gaussian prime a+bi with index k in A103431. k is in A107632 when an integer multiplier m exists such that the distance of m*norm(a+bi) to k is minimal up to k. abs(m*norm(a+bi) - k) is minimal up to k. A107633 gives the squares of the norms of these Gaussian primes, A107634 the integer multipliers m.
A135602: Right-angled numbers with an internal digit as the vertex.
A188135: a(n) = 8*n^2 + 2*n + 1.
A217030: Semiprimes p such that next semiprime after p is p + 10.
A241819: Number of partitions p = [x(1), ..., x(k)], where x(1) >= x(2) >=... >= x(k), of n such that max(x(i) - x(i-1)) <= number of distinct parts of p.

Number of the day: 8163

Properties of the number 8163:

8163 = 3² × 907 is the 7138^th composite number and is not squarefree.
8163 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 5436 totatives.
8163 has a Fibonacci digit product 144 in base 10.
8163 = 10³ + 11³ + 18³ is the sum of 3 positive cubes in 1 way.
8163 = 4082² - 4081² = 1362² - 1359² = 458² - 449² is the difference of 2 nonnegative squares in 3 ways.
8163 is the sum of 2 positive triangular numbers.
8163 is the difference of 2 positive pentagonal numbers in 1 way.
8163 = 5² + 47² + 77² is the sum of 3 positive squares.
8163² is the sum of 3 positive squares.
8163 is a proper divisor of 1291³ - 1.
8163 is palindromic in (at least) the following bases: 25, 41, 48, 51, 77, and -60.
8163 in base 25 = d1d and consists of only the digits '1' and 'd'.
8163 in base 41 = 4Z4 and consists of only the digits '4' and 'Z'.
8163 in base 47 = 3WW and consists of only the digits '3' and 'W'.
8163 in base 48 = 3Q3 and consists of only the digits '3' and 'Q'.
8163 in base 50 = 3DD and consists of only the digits '3' and 'D'.
8163 in base 51 = 373 and consists of only the digits '3' and '7'.

The number 8163 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A037095: "Sloping binary representation" of powers of 3 (A000244), slope = -1.
A046259: a(1) = 9; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A057967: Triangle T(n,k) of numbers of minimal 4-covers of an unlabeled n+4-set that cover k points of that set uniquely (k=4,..,n+4).
A073798: pi(n) is a power of 2, where pi(n) = A000720(n) is the number of primes <= n.
A164399: Number of binary strings of length n with no substrings equal to 0001 or 1010
A178521: The cost of all leaves in the Fibonacci tree of order n.
A206564: Fibonacci sequence beginning 14, 13.
A240726: Number of partitions p of n such that m(p) < m(c(p)), where m = maximal multiplicity of parts, and c = conjugate.
A243717: Number of inequivalent (mod D_4) ways to place 2 nonattacking knights on an n X n board.
A290523: Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 817", based on the 5-celled von Neumann neighborhood.

Number of the day: 717456

Properties of the number 717456:

717456 = 2⁴ × 3 × 14947 is the 659602^th composite number and is not squarefree.
717456 has 3 distinct prime factors, 20 divisors, 3 antidivisors and 239136 totatives.
717456 has a sphenic digit sum 30 in base 10.
717456 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 717456 results in a sphenic number.
717456 = 179365² - 179363² = 89684² - 89680² = 59791² - 59785² = 44845² - 44837² = 29900² - 29888² = 14959² - 14935² is the difference of 2 nonnegative squares in 6 ways.
717456 is the difference of 2 positive pentagonal numbers in 1 way.
717456 = 200² + 316² + 760² is the sum of 3 positive squares.
717456² is the sum of 3 positive squares.
717456 is a proper divisor of 983²⁸² - 1.
717456 in base 3 = 1100110011110 and consists of only the digits '0' and '1'.
717456 in base 43 = 9111 and consists of only the digits '1' and '9'.

Number of the day: 2581

Properties of the number 2581:

2581 is a cyclic number.
2581 = 29 × 89 is semiprime and squarefree.
2581 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 2464 totatives.
2581 = 1291² - 1290² = 59² - 30² is the difference of 2 nonnegative squares in 2 ways.
2581 is the difference of 2 positive pentagonal numbers in 1 way.
2581 = 30² + 41² = 9² + 50² is the sum of 2 positive squares in 2 ways.
2581 = 9² + 14² + 48² is the sum of 3 positive squares.
2581² = 1780² + 1869² = 781² + 2460² = 900² + 2419² = 1131² + 2320² is the sum of 2 positive squares in 4 ways.
2581² is the sum of 3 positive squares.
2581 is a proper divisor of 233⁴ - 1.
2581 is an emirpimes in (at least) the following bases: 3, 4, 15, 16, 17, 20, 25, 31, 33, 36, 37, 38, 41, 42, 44, 46, 48, 49, 51, 52, 54, 56, 58, 63, 65, 66, 69, 70, 72, 75, 77, 78, 83, 91, 93, 94, and 96.
2581 is palindromic in (at least) the following bases: 18, 43, 88, -23, -60, and -86.
2581 in base 18 = 7h7 and consists of only the digits '7' and 'h'.
2581 in base 22 = 577 and consists of only the digits '5' and '7'.
2581 in base 42 = 1JJ and consists of only the digits '1' and 'J'.
2581 in base 43 = 1H1 and consists of only the digits '1' and 'H'.
2581 in base 50 = 11V and consists of only the digits '1' and 'V'.

The number 2581 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006327: a(n) = Fibonacci(n) - 3. Number of total preorders.
A017981: Powers of cube root of 2 rounded up.
A017987: Powers of cube root of 4 rounded up.
A045944: Rhombic matchstick numbers: a(n) = n*(3*n+2).
A151725: Number of ON states after n generations of cellular automaton based on square grid with each cell adjacent to its eight neighbors.
A214119: Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 2, n >= 2.
A252167: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum equal to 2 3 4 6 or 7 and every 3X3 diagonal and antidiagonal sum not equal to 2 3 4 6 or 7
A256075: Non-palindromic balanced numbers (in base 10).
A326512: Number of set partitions of {1..n} where every block has the same average.
A326977: Number of integer partitions of n such that the dual of the multiset partition obtained by factoring each part into prime numbers is a (strict) antichain, also called T_1 integer partitions.

Number of the day: 21428007622

Properties of the number 21428007622:

21428007622 = 2 × 7² × 463 × 472253 is composite and not squarefree.
21428007622 has 4 distinct prime factors, 24 divisors, 27 antidivisors and 9163577808 totatives.
21428007622 has a semiprime digit sum 34 in base 10.
21428007622 has a Fibonacci digit sum 34 in base 10.
21428007622 is the difference of 2 positive pentagonal numbers in 12 ways.
21428007622 = 2021² + 2034² + 146355² is the sum of 3 positive squares.
21428007622² = 7249494728² + 20164432470² is the sum of 2 positive squares in 1 way.
21428007622² is the sum of 3 positive squares.
21428007622 is a proper divisor of 557⁷⁰⁸³⁷⁸ - 1.

Number of the day: 3193

Marius Sophus Lie was born on this day 178 years ago.

Properties of the number 3193:

3193 is a cyclic number.
3193 = 31 × 103 is semiprime and squarefree.
3193 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 3060 totatives.
Reversing the decimal digits of 3193 results in a sphenic number.
3193 = 1597² - 1596² = 67² - 36² is the difference of 2 nonnegative squares in 2 ways.
3193 is the sum of 2 positive triangular numbers.
3193 is the difference of 2 positive pentagonal numbers in 2 ways.
3193 = 9² + 14² + 54² is the sum of 3 positive squares.
3193² is the sum of 3 positive squares.
3193 is a proper divisor of 619² - 1.
3193 = '3' + '193' is the concatenation of 2 prime numbers.
3193 is an emirpimes in (at least) the following bases: 8, 9, 20, 21, 23, 24, 27, 32, 35, 39, 41, 45, 47, 52, 53, 61, 63, 67, 69, 73, 76, 77, 84, 85, 91, 94, 95, 96, 97, and 99.
3193 is palindromic in (at least) the following bases: 29, 42, 56, -57, -76, and -84.
3193 in base 7 = 12211 and consists of only the digits '1' and '2'.
3193 in base 29 = 3n3 and consists of only the digits '3' and 'n'.
3193 in base 32 = 33p and consists of only the digits '3' and 'p'.
3193 in base 41 = 1aa and consists of only the digits '1' and 'a'.
3193 in base 42 = 1Y1 and consists of only the digits '1' and 'Y'.
3193 in base 55 = 133 and consists of only the digits '1' and '3'.
3193 in base 56 = 111 and consists of only the digit '1'.

The number 3193 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001595: a(n) = a(n-1) + a(n-2) + 1, with a(0) = a(1) = 1.
A054569: a(n) = 4*n^2 - 6*n + 3.
A062114: a(n) = 2*Fibonacci(n) - (1 - (-1)^n)/2.
A062668: Composite and every divisor (except 1) contains the digit 3.
A066983: a(n+2) = a(n+1) + a(n) + (-1)^n, with a(1) = a(2) = 1.
A099971: Write (sqrt(5)-1)/2 as a binary fraction; read this from left to right and whenever a 1 appears, note the integer formed by reading leftwards from that 1.
A144781: Variant of Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(1) = 8.
A161532: a(n) = 2n^2 + 8n + 1.
A277699: Main diagonal of A277320: a(n) = A048720(n, A065621(n)).
A325534: Number of separable partitions of n; see Comments.

Number of the day: 635277

Happy Pythagorean Theorem Day!

Properties of the number 635277:

635277 = 3 × 367 × 577 is a sphenic number and squarefree.
635277 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 421632 totatives.
635277 has a sphenic digit sum 30 in base 10.
635277 has an oblong digit sum 30 in base 10.
635277 = 317639² - 317638² = 105881² - 105878² = 1049² - 682² = 839² - 262² is the difference of 2 nonnegative squares in 4 ways.
635277 is the difference of 2 positive pentagonal numbers in 1 way.
635277 = 19² + 104² + 790² is the sum of 3 positive squares.
635277² = 52848² + 633075² is the sum of 2 positive squares in 1 way.
635277² is the sum of 3 positive squares.
635277 is a proper divisor of 1153¹²² - 1.
635277 = '63527' + '7' is the concatenation of 2 prime numbers.

Number of the day: 649

János Bolyai was born on this day 218 years ago.

Properties of the number 649:

649 is a cyclic number.
649 = 11 × 59 is semiprime and squarefree.
649 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 580 totatives.
649 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 649 results in a sphenic number.
Reversing the decimal digits of 649 results in a triangular number.
649 = 2² + … + 12² is the sum of at least 2 consecutive positive squares in 1 way.
649 = 325² - 324² = 35² - 24² is the difference of 2 nonnegative squares in 2 ways.
649 is the sum of 2 positive triangular numbers.
649 is the difference of 2 positive pentagonal numbers in 1 way.
649 = 3² + 8² + 24² is the sum of 3 positive squares.
649² is the sum of 3 positive squares.
649 is a proper divisor of 353² - 1.
649 = '6' + '49' is the concatenation of 2 semiprime numbers.
649 is an emirpimes in (at least) the following bases: 2, 4, 6, 7, 11, 16, 18, 19, 20, 23, 25, 26, 27, 29, 30, 33, 34, 42, 43, 44, 45, 47, 50, 63, 64, 65, 66, 67, 69, 70, 74, 75, 79, 82, 84, 87, 88, 89, 90, 91, and 97.
649 is palindromic in (at least) the following bases: 24, 58, -8, -17, -27, -36, -54, -72, and -81.
649 in base 8 = 1211 and consists of only the digits '1' and '2'.
649 in base 23 = 155 and consists of only the digits '1' and '5'.
649 in base 24 = 131 and consists of only the digits '1' and '3'.

The number 649 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000960: Flavius Josephus's sieve: Start with the natural numbers; at the k-th sieving step, remove every (k+1)-st term of the sequence remaining after the (k-1)-st sieving step; iterate.
A003355: Numbers that are the sum of 10 positive 5th powers.
A024206: Expansion of x^2*(1+x-x^2)/((1-x^2)*(1-x)^2).
A028387: a(n) = n + (n+1)^2.
A051424: Number of partitions of n into pairwise relatively prime parts.
A058331: a(n) = 2*n^2 + 1.
A078972: Brilliant numbers: semiprimes (products of two primes, A001358) whose prime factors have the same number of decimal digits.
A166459: Numbers whose sum of digits is 19.
A195162: Generalized 12-gonal numbers: k*(5*k-4) for k = 0, +-1, +-2, ...
A333218: Numbers k such that the k-th composition in standard order is a permutation (of an initial interval).

Number of the day: 15604

Properties of the number 15604:

15604 = 2² × 47 × 83 is the 13784^th composite number and is not squarefree.
15604 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 7544 totatives.
Reversing the decimal digits of 15604 results in a sphenic number.
15604 = 3902² - 3900² = 130² - 36² is the difference of 2 nonnegative squares in 2 ways.
15604 is the sum of 2 positive triangular numbers.
15604 is the difference of 2 positive pentagonal numbers in 1 way.
15604 = 42² + 68² + 96² is the sum of 3 positive squares.
15604² is the sum of 3 positive squares.
15604 is a proper divisor of 941⁴¹ - 1.
15604 is palindromic in (at least) the following bases: 60, -8, and -65.
15604 in base 5 = 444404 and consists of only the digits '0' and '4'.
15604 in base 25 = oo4 and consists of only the digits '4' and 'o'.
15604 in base 39 = AA4 and consists of only the digits '4' and 'A'.
15604 in base 59 = 4SS and consists of only the digits '4' and 'S'.
15604 in base 60 = 4K4 and consists of only the digits '4' and 'K'.

The number 15604 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A042521: Denominators of continued fraction convergents to sqrt(789).
A101580: Indices of primes in sequence defined by A(0) = 57, A(n) = 10*A(n-1) - 23 for n > 0.
A120914: Cascadence of (1+2x)^2; a triangle, read by rows of 2n+1 terms, that retains its original form upon convolving each row with [1,4,4] and then letting excess terms spill over from each row into the initial positions of the next row such that only 2n+1 terms remain in row n for n>=0.
A235192: Number of (n+1)X(2+1) 0..6 arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 5, with no adjacent elements equal (constant stress tilted 1X1 tilings)
A235194: Number of (n+1)X(4+1) 0..6 arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 5, with no adjacent elements equal (constant stress tilted 1X1 tilings)
A235198: T(n,k)=Number of (n+1)X(k+1) 0..6 arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 5, with no adjacent elements equal (constant stress tilted 1X1 tilings)
A259487: Least positive integer m with prime(m)+2 and prime(prime(m))+2 both prime such that prime(m*n)+2 and prime(prime(m*n))+2 are both prime.
A281992: Numbers k such that (2*10^k - 143)/3 is prime.
A294867: Solution of the complementary equation a(n) = 2*a(n-1) - a(n-2) + b(n-1) -1, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
A304666: Number of nX5 0..1 arrays with every element unequal to 0, 1, 3, 5 or 6 king-move adjacent elements, with upper left element zero.

Number of the day: 849377179

Properties of the number 849377179:

849377179 = 7 × 121339597 is semiprime and squarefree.
849377179 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 728037576 totatives.
849377179 has a semiprime digit sum 55 in base 10.
849377179 has a Fibonacci digit sum 55 in base 10.
849377179 has a triangular digit sum 55 in base 10.
849377179 = 424688590² - 424688589² = 60669802² - 60669795² is the difference of 2 nonnegative squares in 2 ways.
849377179 is the sum of 2 positive triangular numbers.
849377179 is the difference of 2 positive pentagonal numbers in 2 ways.
849377179 = 827² + 1005² + 29115² is the sum of 3 positive squares.
849377179² = 500175396² + 686488285² is the sum of 2 positive squares in 1 way.
849377179² is the sum of 3 positive squares.
849377179 is a proper divisor of 751¹⁴⁹⁴³³ - 1.
849377179 = '84937' + '7179' is the concatenation of 2 semiprime numbers.
849377179 is an emirpimes in (at least) the following bases: 2, 9, 12, 13, 15, 19, 23, 29, 31, 32, 37, 44, 47, 49, 51, 56, 57, 62, 65, 76, 83, 88, 89, 93, 97, and 99.

Number of the day: 17716

Carl Gustav Jacob Jacobi was born on this day 216 years ago.

Properties of the number 17716:

(17716, 14316, 19116, 31704, 47616, 83328, 177792, 295488, 629072, 589786, 294896, 358336, 418904, 366556, 274924, 275444, 243760, 376736, 381028, 285778, 152990, 122410, 97946, 48976, 45946, 22976, 22744, 19916) is a cycle of sociable numbers of length 28.
17716 = 2² × 43 × 103 is the 15681^th composite number and is not squarefree.
17716 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 8568 totatives.
17716 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 17716 results in a semiprime.
17716 = 4430² - 4428² = 146² - 60² is the difference of 2 nonnegative squares in 2 ways.
17716 is the sum of 2 positive triangular numbers.
17716 is the difference of 2 positive pentagonal numbers in 3 ways.
17716 = 6² + 16² + 132² is the sum of 3 positive squares.
17716² is the sum of 3 positive squares.
17716 is a proper divisor of 1031² - 1.
17716 is palindromic in (at least) the following bases: -55, and -72.
17716 in base 14 = 6656 and consists of only the digits '5' and '6'.
17716 in base 54 = 644 and consists of only the digits '4' and '6'.
17716 in base 59 = 55G and consists of only the digits '5' and 'G'.

The number 17716 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A045247: Numbers n with property that in base 5 representation the numbers of 1's and 3's are 3 and 3, respectively.
A072890: The 28-cycle of the n => sigma(n)-n process, where sigma(n) is the sum of divisors of n (A000203).
A122726: Sociable numbers.
A157729: a(n) = Fibonacci(n) + 5.
A187670: T(n,k)=Number of (n+1)X(n+1) 0..k arrays with each 2X2 subblock nonsingular and the array of 2X2 subblock determinants symmetric about the diagonal and antidiagonal
A187671: Number of 3X3 0..n arrays with each 2X2 subblock nonsingular and the array of 2X2 subblock determinants symmetric about the diagonal and antidiagonal
A229577: Number of defective 4-colorings of an n X 7 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..3 order.
A244714: Number of compositions of n with exactly 2 transitions between different parts.
A274163: Number of real integers in n-th generation of tree T(4i) defined in Comments.
A323348: Number of integer partitions of n whose parts cannot be arranged into a (not necessarily square) matrix with equal row-sums and equal column-sums.

Number of the day: 281712226896

Properties of the number 281712226896:

281712226896 = 2⁴ × 3² × 47 × 41624147 is composite and not squarefree.
281712226896 has 4 distinct prime factors, 60 divisors, 15 antidivisors and 91906114368 totatives.
281712226896 = 4092³ + 4418³ + 5026³ is the sum of 3 positive cubes in 1 way.
281712226896 is the difference of 2 nonnegative squares in 18 ways.
281712226896 is the difference of 2 positive pentagonal numbers in 2 ways.
281712226896 = 1276² + 11104² + 530648² is the sum of 3 positive squares.
281712226896² is the sum of 3 positive squares.
281712226896 is a proper divisor of 109^11067692 - 1.

Number of the day: 169087

Jacques Salomon Hadamard was born on this day 155 years ago.

Julia Robinson was born on this day 101 years ago.

Properties of the number 169087:

169087 is a cyclic number.
169087 = 353 × 479 is semiprime and squarefree.
169087 has 2 distinct prime factors, 4 divisors, 37 antidivisors and 168256 totatives.
169087 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 169087 results in a prime.
169087 = 84544² - 84543² = 416² - 63² is the difference of 2 nonnegative squares in 2 ways.
169087 is the sum of 2 positive triangular numbers.
169087 is the difference of 2 positive pentagonal numbers in 1 way.
169087 is not the sum of 3 positive squares.
169087² = 107775² + 130288² is the sum of 2 positive squares in 1 way.
169087² is the sum of 3 positive squares.
169087 is a proper divisor of 311⁹⁵⁶ - 1.
169087 is an emirpimes in (at least) the following bases: 2, 4, 5, 8, 11, 14, 17, 20, 23, 25, 32, 33, 35, 44, 45, 47, 52, 57, 62, 67, 71, 73, 76, 77, 78, 80, 81, 82, 85, 88, 89, 93, 94, and 98.
169087 is palindromic in (at least) base 79.
169087 in base 38 = 333P and consists of only the digits '3' and 'P'.

The number 169087 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A248880: Number of tilings of an n X 1 rectangle by tiles of dimension 1 X 1 and 2 X 1 such that every tile shares an equal-length edge with a tile of the same size.

Number of the day: 780311

Leopold Kronecker was born on this day 197 years ago.

Properties of the number 780311:

780311 = 7 × 19 × 5867 is a sphenic number and squarefree.
780311 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 633528 totatives.
780311 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 780311 results in a semiprime.
780311 = 390156² - 390155² = 55740² - 55733² = 20544² - 20525² = 3000² - 2867² is the difference of 2 nonnegative squares in 4 ways.
780311 is the difference of 2 positive pentagonal numbers in 4 ways.
780311 is not the sum of 3 positive squares.
780311² is the sum of 3 positive squares.
780311 is a proper divisor of 1217⁸³⁸ - 1.

Number of the day: 62093

Properties of the number 62093:

62093 is a cyclic number.
62093 = 31 × 2003 is semiprime and squarefree.
62093 has 2 distinct prime factors, 4 divisors, 23 antidivisors and 60060 totatives.
62093 has an oblong digit sum 20 in base 10.
62093 = 31047² - 31046² = 1017² - 986² is the difference of 2 nonnegative squares in 2 ways.
62093 is the difference of 2 positive pentagonal numbers in 2 ways.
62093 = 21² + 46² + 244² is the sum of 3 positive squares.
62093² is the sum of 3 positive squares.
62093 is a proper divisor of 1117²² - 1.
62093 is an emirpimes in (at least) the following bases: 2, 3, 9, 11, 14, 17, 19, 23, 27, 29, 31, 32, 34, 40, 42, 47, 48, 49, 50, 51, 53, 55, 56, 58, 59, 61, 64, 67, 68, 70, 76, 79, 80, 82, 87, 89, 90, 92, 93, 95, 97, and 99.
62093 is palindromic in (at least) the following bases: 83, and -57.
62093 in base 18 = abbb and consists of only the digits 'a' and 'b'.

The number 62093 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A053391: Number of cycle types of direct products of two degree-n permutations.
A107586: Powers of e^(1/e) rounded up.
A128368: a(n) = least k such that the remainder when 28^k is divided by k is n.
A219898: Record values in A214551.

Number of the day: 3839165

Nikolai Lobachevsky was born on this day 228 years ago.

Properties of the number 3839165:

3839165 = 5 × 11 × 29² × 83 is the 3566576^th composite number and is not squarefree.
3839165 has 4 distinct prime factors, 24 divisors, 29 antidivisors and 2663360 totatives.
3839165 has a semiprime digit sum 35 in base 10.
3839165 is the difference of 2 nonnegative squares in 12 ways.
3839165 is the difference of 2 positive pentagonal numbers in 10 ways.
3839165 = 2² + 115² + 1956² is the sum of 3 positive squares.
3839165² = 2303499² + 3071332² = 635448² + 3786211² = 450109² + 3812688² = 2151028² + 3179979² = 2450492² + 2955381² = 2647700² + 2780085² = 187165² + 3834600² is the sum of 2 positive squares in 7 ways.
3839165² is the sum of 3 positive squares.
3839165 is a proper divisor of 331¹¹⁶ - 1.
3839165 is palindromic in (at least) base -30.

Number of the day: 79103

Properties of the number 79103:

79103 is a cyclic number.
79103 is the 7752^th prime.
79103 has 21 antidivisors and 79102 totatives.
79103 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 79103 results in an emirp.
79103 = 39552² - 39551² is the difference of 2 nonnegative squares in 1 way.
79103 is the difference of 2 positive pentagonal numbers in 1 way.
79103 is not the sum of 3 positive squares.
79103² is the sum of 3 positive squares.
79103 is a proper divisor of 2³⁹⁵⁵¹ - 1.
79103 = '7' + '9103' is the concatenation of 2 prime numbers.
79103 is an emirp in (at least) the following bases: 2, 6, 7, 10, 15, 17, 23, 24, 27, 29, 41, 49, 52, 55, 58, 59, 65, 67, 69, 73, 76, 77, and 100.

The number 79103 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A113893: Smallest prime obtained as a concatenation of prime(n) and prime(m) with m > n.

Number of the day: 56493

Properties of the number 56493:

56493 = 3² × 6277 is the 50764^th composite number and is not squarefree.
56493 has 2 distinct prime factors, 6 divisors, 13 antidivisors and 37656 totatives.
56493 has a triangular digit product 3240 in base 10.
56493 = 2³ + 18³ + 37³ is the sum of 3 positive cubes in 1 way.
56493 = 28247² - 28246² = 9417² - 9414² = 3143² - 3134² is the difference of 2 nonnegative squares in 3 ways.
56493 is the difference of 2 positive pentagonal numbers in 1 way.
56493 = 18² + 237² is the sum of 2 positive squares in 1 way.
56493 = 11² + 26² + 236² is the sum of 3 positive squares.
56493² = 8532² + 55845² is the sum of 2 positive squares in 1 way.
56493² is the sum of 3 positive squares.
56493 is a proper divisor of 1033¹² - 1.
56493 is palindromic in (at least) the following bases: 67, and -52.
56493 in base 6 = 1113313 and consists of only the digits '1' and '3'.
56493 in base 48 = OOj and consists of only the digits 'O' and 'j'.
56493 in base 51 = Laa and consists of only the digits 'L' and 'a'.

The number 56493 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A322569: a(n)=x is the least integer such that gcd(sigma(x), sigma(x+1)) = 2*n.

Number of the day: 7335228

Properties of the number 7335228:

7335228 = 2² × 3 × 17 × 41 × 877 is the 6837343^th composite number and is not squarefree.
7335228 has 5 distinct prime factors, 48 divisors, 17 antidivisors and 2242560 totatives.
7335228 has a sphenic digit sum 30 in base 10.
7335228 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 7335228 results in a semiprime.
7335228 = 1833808² - 1833806² = 611272² - 611266² = 107888² - 107854² = 44768² - 44686² = 36008² - 35906² = 15032² - 14786² = 3328² - 1934² = 2968² - 1214² is the difference of 2 nonnegative squares in 8 ways.
7335228 is the difference of 2 positive pentagonal numbers in 4 ways.
7335228 is not the sum of 3 positive squares.
7335228² = 4571172² + 5736720² = 3451872² + 6472260² = 600240² + 7310628² = 4593372² + 5718960² = 1946940² + 7072128² = 1019172² + 7264080² = 4788420² + 5556672² = 3200400² + 6600228² = 2190372² + 7000560² = 4317660² + 5929872² = 1610172² + 7156320² = 1361700² + 7207728² = 2910672² + 6733020² is the sum of 2 positive squares in 13 ways.
7335228² is the sum of 3 positive squares.
7335228 is a proper divisor of 151⁴⁰ - 1.

Number of the day: 727733159

Properties of the number 727733159:

727733159 is a cyclic number.
727733159 = 109 × 6676451 is semiprime and squarefree.
727733159 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 721056600 totatives.
Reversing the decimal digits of 727733159 results in a sphenic number.
727733159 = 363866580² - 363866579² = 3338280² - 3338171² is the difference of 2 nonnegative squares in 2 ways.
727733159 is the difference of 2 positive pentagonal numbers in 2 ways.
727733159 is not the sum of 3 positive squares.
727733159² = 400587060² + 607557041² is the sum of 2 positive squares in 1 way.
727733159² is the sum of 3 positive squares.
727733159 is a proper divisor of 499¹⁶⁴¹⁷⁵ - 1.
727733159 = '7' + '27733159' is the concatenation of 2 prime numbers.
727733159 is an emirpimes in (at least) the following bases: 2, 4, 5, 8, 9, 14, 19, 25, 28, 32, 35, 40, 42, 48, 51, 54, 56, 57, 59, 63, 64, 69, 71, 80, 81, 86, 90, and 94.

Number of the day: 4826

Norbert Wiener was born on this day 126 years ago.

Properties of the number 4826:

4826 = 2 × 19 × 127 is a sphenic number and squarefree.
4826 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 2268 totatives.
4826 has an oblong digit sum 20 in base 10.
4826 = 1³ + 9³ + 16³ is the sum of 3 positive cubes in 1 way.
4826 = 9² + 16² + 67² is the sum of 3 positive squares.
4826² is the sum of 3 positive squares.
4826 is a proper divisor of 761² - 1.
4826 = '482' + '6' is the concatenation of 2 semiprime numbers.
4826 is palindromic in (at least) base -67.

The number 4826 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003359: Numbers that are the sum of 3 nonzero 6th powers.
A025414: a(n) is the smallest number that is the sum of 3 nonzero squares in exactly n ways.
A051989: Discriminants of real quadratic fields with class number 2 and related continued fraction period length of 24.
A071609: Squared radii of the spheres around (0,0,0) that contain record numbers of lattice points.
A091710: Number of primes less than 10^n having at least one digit 9.
A092265: Sum of smallest parts of all partitions of n into distinct parts.
A095809: Least positive number having exactly n partitions into three squares.
A237859: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors
A278180: Square spiral in which each new term is the sum of its two largest neighbors.
A324703: Lexicographically earliest sequence containing 3 and all positive integers n such that the prime indices of n - 1 already belong to the sequence.

Number of the day: 9699

Properties of the number 9699:

9699 = 3 × 53 × 61 is a sphenic number and squarefree.
9699 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 6240 totatives.
9699 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 9699 results in a semiprime.
9699 = 4850² - 4849² = 1618² - 1615² = 118² - 65² = 110² - 49² is the difference of 2 nonnegative squares in 4 ways.
9699 is the difference of 2 positive pentagonal numbers in 1 way.
9699 = 7² + 25² + 95² is the sum of 3 positive squares.
9699² = 5124² + 8235² = 3555² + 9024² = 6525² + 7176² = 1749² + 9540² is the sum of 2 positive squares in 4 ways.
9699² is the sum of 3 positive squares.
9699 is a proper divisor of 743⁴ - 1.
9699 = '9' + '699' is the concatenation of 2 semiprime numbers.
9699 is palindromic in (at least) base -34.
9699 consists of only the digits '6' and '9'.

The number 9699 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033572: a(n) = (2*n+1)*(7*n+1).
A059610: Numbers n such that 2^n - 9 is prime.
A062185: Harmonic mean of digits is 8.
A074343: a(1) = 7; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A111494: 3-almost primes with semiprime digits (digits 4, 6, 9 only).
A114615: Starting numbers for which the RATS sequence has eventual period 14.
A178369: Numbers with rounded up arithmetic mean of digits = 9.
A259487: Least positive integer m with prime(m)+2 and prime(prime(m))+2 both prime such that prime(m*n)+2 and prime(prime(m*n))+2 are both prime.
A286444: Number of non-equivalent ways to tile an n X n X n triangular area with two 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-8) of 1 X 1 X 1 tiles.
A292739: Numbers in which 9 outnumbers all other digits together.

Number of the day: 11232020

John Wallis was born on this day 404 years ago.

Happy Fibonacci Day!

Properties of the number 11232020:

11232020 = 2² × 5 × 433 × 1297 is the 10491199^th composite number and is not squarefree.
11232020 has 4 distinct prime factors, 24 divisors, 13 antidivisors and 4478976 totatives.
11232020 has a prime digit sum 11 in base 10.
11232020 = 2808006² - 2808004² = 561606² - 561596² = 6918² - 6052² = 3462² - 868² is the difference of 2 nonnegative squares in 4 ways.
11232020 is the difference of 2 positive pentagonal numbers in 3 ways.
11232020 = 1666² + 2908² = 1502² + 2996² = 596² + 3298² = 412² + 3326² is the sum of 2 positive squares in 4 ways.
11232020 = 20² + 222² + 3344² is the sum of 3 positive squares.
11232020² = 7227636² + 8597648² = 6739212² + 8985616² = 6230004² + 9345872² = 3931216² + 10521588² = 3341072² + 10723596² = 2740624² + 10892532² = 6720012² + 8999984² = 6210036² + 9359152² = 5680908² + 9689456² = 4343020² + 10358400² = 3761300² + 10583520² = 3167980² + 10776000² = 623520² + 11214700² is the sum of 2 positive squares in 13 ways.
11232020² is the sum of 3 positive squares.
11232020 is a proper divisor of 1291²⁴ - 1.

Number of the day: 34443

Émile Michel Hyacinthe Lemoine was born on this day 180 years ago.

Properties of the number 34443:

34443 = 3² × 43 × 89 is the 30763^th composite number and is not squarefree.
34443 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 22176 totatives.
34443 = 17222² - 17221² = 5742² - 5739² = 1918² - 1909² = 422² - 379² = 238² - 149² = 198² - 69² is the difference of 2 nonnegative squares in 6 ways.
34443 is the difference of 2 positive pentagonal numbers in 1 way.
34443 = 7² + 13² + 185² is the sum of 3 positive squares.
34443² = 15093² + 30960² is the sum of 2 positive squares in 1 way.
34443² is the sum of 3 positive squares.
34443 is a proper divisor of 179⁶ - 1.
34443 is a palindrome (in base 10).
34443 is palindromic in (at least) base -36.
34443 consists of only the digits '3' and '4'.
34443 in base 40 = LL3 and consists of only the digits '3' and 'L'.
34443 in base 41 = KK3 and consists of only the digits '3' and 'K'.

The number 34443 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006341: Octal palindromes which are also primes.
A041657: Denominators of continued fraction convergents to sqrt(347).
A077291: Second member of Diophantine pair (m,k) that satisfies 6*(m^2 + m) = k^2 + k: a(n) = k.
A077741: Smallest multiple of n which begins with R(n) and ends in n where R(n) (A004086) is the digit reversal of n. Suitable number of zeros are assumed to the left of the MSD if required.
A082394: Let p = n-th prime of the form 4k+3, take the solution (x,y) to the Pellian equation x^2 - p*y^2 = 1 with x and smallest y >= 1; sequence gives value of y.
A084008: a(n) = T(n) concatenated with reverse(T(n)) divided by 11, where T(n) is the n-th triangular number.
A094625: Expansion of x*(2+22*x+11*x^2)/((x-1)*(1+x)*(10*x^2-1)).
A095294: Number of A095284-primes in range ]2^n,2^(n+1)].
A096025: Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 6 and (n+7) mod 9 <> 1.
A175760: Numbers n such that d(n + d(n)) = d(n), where d(n) is the sum of the distinct primes dividing n.

Number of the day: 7247

Benoit Mandelbrot was born on this day 96 years ago.

Properties of the number 7247:

7247 is a cyclic number.
7247 is the 927^th prime.
7247 has 9 antidivisors and 7246 totatives.
7247 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 7247 results in a semiprime.
7247 = 3624² - 3623² is the difference of 2 nonnegative squares in 1 way.
7247 is the sum of 2 positive triangular numbers.
7247 is the difference of 2 positive pentagonal numbers in 1 way.
7247 is not the sum of 3 positive squares.
7247² is the sum of 3 positive squares.
7247 is a proper divisor of 2³⁶²³ - 1.
7247 is an emirp in (at least) the following bases: 6, 7, 8, 13, 15, 18, 21, 23, 29, 31, 36, 38, 39, 43, 46, 53, 64, 65, 67, 68, 69, 70, 71, 79, 80, 81, 84, 89, 98, and 99.
7247 is palindromic in (at least) the following bases: -63, and -69.
7247 in base 15 = 2232 and consists of only the digits '2' and '3'.
7247 in base 19 = 1118 and consists of only the digits '1' and '8'.
7247 in base 42 = 44N and consists of only the digits '4' and 'N'.

The number 7247 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A026378: a(n) = number of integer strings s(0),...,s(n) counted by array T in A026374 that have s(n)=1; also a(n) = T(2n-1,n-1).
A045713: Primes with first digit 7.
A066179: Primes p such that (p-1)/2 and (p-3)/4 are also prime.
A073609: a(0) = 2; a(n) for n > 0 is the smallest prime greater than a(n-1) that differs from a(n-1) by a square.
A075421: Trajectory of n under the Reverse and Add! operation carried out in base 4 (presumably) does not reach a palindrome and (presumably) does not join the trajectory of any term m < n.
A104845: Primes from merging of 4 successive digits in decimal expansion of e.
A126791: Binomial matrix applied to A111418.
A141908: Primes congruent to 2 mod 23.
A198778: Primes from merging of 4 successive digits in decimal expansion of Euler-Mascheroni constant A001620.
A238583: Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 9 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=2*floor(n/4), read by rows.

Number of the day: 5148

Properties of the number 5148:

5148 is the 1294^th totient number.
5148 = 2² × 3² × 11 × 13 is the 4461^th composite number and is not squarefree.
5148 has 4 distinct prime factors, 36 divisors, 19 antidivisors and 1440 totatives.
5148 = 1288² - 1286² = 432² - 426² = 152² - 134² = 128² - 106² = 112² - 86² = 72² - 6² is the difference of 2 nonnegative squares in 6 ways.
5148 is the sum of 2 positive triangular numbers.
5148 is not the sum of 3 positive squares.
5148² = 1980² + 4752² is the sum of 2 positive squares in 1 way.
5148² is the sum of 3 positive squares.
5148 is a proper divisor of 1871² - 1.
5148 is palindromic in (at least) the following bases: 77, 98, -49, and -62.
5148 in base 50 = 22m and consists of only the digits '2' and 'm'.

The number 5148 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006011: a(n) = n^2*(n^2 - 1)/4.
A028723: a(n) = (1/4)*floor(n/2)*floor((n-1)/2)*floor((n-2)/2)*floor((n-3)/2).
A029651: Central elements of the (1,2)-Pascal triangle A029635.
A033991: a(n) = n*(4*n-1).
A045873: a(n) = A006496(n)/2.
A050486: a(n) = binomial(n+6,6)*(2n+7)/7.
A111125: Triangle read by rows: T(k,s) = ((2*k+1)/(2*s+1))*binomial(k+s,2*s), 0 <= s <= k.
A200192: T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing
A213697: T(n,k)=Half the number of (n+1)X(n+1) symmetric 0..k arrays with no 2X2 subblock summing to 2k
A247726: T(n,k)=Number of length n+3 0..k arrays with no disjoint pairs in any consecutive four terms having the same sum

Number of the day: 95868

Properties of the number 95868:

95868 = 2² × 3² × 2663 is the 86629^th composite number and is not squarefree.
95868 has 3 distinct prime factors, 18 divisors, 25 antidivisors and 31944 totatives.
95868 has a triangular digit sum 36 in base 10.
95868 = 23968² - 23966² = 7992² - 7986² = 2672² - 2654² is the difference of 2 nonnegative squares in 3 ways.
95868 is the difference of 2 positive pentagonal numbers in 1 way.
95868 is not the sum of 3 positive squares.
95868² is the sum of 3 positive squares.
95868 is a proper divisor of 37¹¹ - 1.
95868 is palindromic in (at least) the following bases: -37, and -75.
95868 in base 37 = 1X11 and consists of only the digits '1' and 'X'.
95868 in base 58 = SSq and consists of only the digits 'S' and 'q'.

Number of the day: 16585014736

August Ferdinand Möbius was born on this day 230 years ago.

Properties of the number 16585014736:

16585014736 = 2⁴ × 12049 × 86029 is composite and not squarefree.
16585014736 has 3 distinct prime factors, 20 divisors, 51 antidivisors and 8291722752 totatives.
16585014736 has a semiprime digit sum 46 in base 10.
Reversing the decimal digits of 16585014736 results in a sphenic number.
16585014736 = 4146253685² - 4146253683² = 2073126844² - 2073126840² = 1036563425² - 1036563417² = 356165² - 332067² = 196156² - 147960² = 134225² - 37833² is the difference of 2 nonnegative squares in 6 ways.
16585014736 is the sum of 2 positive triangular numbers.
16585014736 is the difference of 2 positive pentagonal numbers in 3 ways.
16585014736 = 78040² + 102444² = 7640² + 128556² is the sum of 2 positive squares in 2 ways.
16585014736 = 144² + 2420² + 128760² is the sum of 3 positive squares.
16585014736² = 9249838080² + 13766016464² = 4404531536² + 15989459520² = 1964335680² + 16468275536² = 10815182400² + 12573565264² is the sum of 2 positive squares in 4 ways.
16585014736² is the sum of 3 positive squares.
16585014736 is a proper divisor of 1301⁶⁷²⁶⁸ - 1.
16585014736 = '1658501473' + '6' is the concatenation of 2 semiprime numbers.

Number of the day: 21478

Properties of the number 21478:

21478 = 2 × 10739 is semiprime and squarefree.
21478 has 2 distinct prime factors, 4 divisors, 25 antidivisors and 10738 totatives.
21478 has a semiprime digit sum 22 in base 10.
21478 has sum of divisors equal to 32220 which is an oblong number.
21478 is the sum of 2 positive triangular numbers.
21478 is the difference of 2 positive pentagonal numbers in 2 ways.
21478 = 21² + 34² + 141² is the sum of 3 positive squares.
21478² is the sum of 3 positive squares.
21478 is a proper divisor of 853⁵⁹ - 1.
21478 = '21' + '478' is the concatenation of 2 semiprime numbers.
21478 is an emirpimes in (at least) the following bases: 2, 8, 11, 13, 14, 16, 17, 18, 20, 21, 24, 26, 28, 30, 31, 35, 37, 39, 40, 41, 43, 46, 50, 51, 53, 55, 59, 63, 64, 69, 74, 76, 82, 84, 89, 92, and 95.
21478 is palindromic in (at least) the following bases: 91, and -61.

The number 21478 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A024588: a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n+1-k), where k = [ (n+1)/2 ], s = (composite numbers).
A092310: Sum of largest parts (counted with multiplicity) of all partitions of n into odd parts.
A116705: Number of permutations of length n which avoid the patterns 1234, 4312.
A187378: Number of 4-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions
A229063: Volume of the Johnson square pyramid (rounded down) with all the edge lengths equal to n.
A304384: a(n) = 168*2^n - 26 (n>=1).