Number of the day: 741593

Properties of the number 741593:

741593 is a cyclic number.
741593 is the 59644^th prime.
741593 has 31 antidivisors and 741592 totatives.
741593 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 741593 results in an emirp.
741593 = 54³ + 58³ + 73³ is the sum of 3 positive cubes in 1 way.
741593 = 370797² - 370796² is the difference of 2 nonnegative squares in 1 way.
741593 is the sum of 2 positive triangular numbers.
741593 is the difference of 2 positive pentagonal numbers in 1 way.
741593 = 452² + 733² is the sum of 2 positive squares in 1 way.
741593 = 12² + 43² + 860² is the sum of 3 positive squares.
741593² = 332985² + 662632² is the sum of 2 positive squares in 1 way.
741593² is the sum of 3 positive squares.
741593 is a proper divisor of 47⁹²⁶⁹⁹ - 1.
741593 = '7' + '41593' is the concatenation of 2 prime numbers.
741593 = '7415' + '93' is the concatenation of 2 semiprime numbers.
741593 is an emirp in (at least) the following bases: 7, 10, 18, 26, 28, 40, 49, 55, 57, 76, 84, 85, 88, 93, and 94.

Number of the day: 88655022

Properties of the number 88655022:

88655022 = 2 × 3² × 421 × 11699 is the 83511370^th composite number and is not squarefree.
88655022 has 4 distinct prime factors, 24 divisors, 41 antidivisors and 29478960 totatives.
88655022 has a triangular digit sum 36 in base 10.
88655022 is the sum of 2 positive triangular numbers.
88655022 is the difference of 2 positive pentagonal numbers in 3 ways.
88655022 = 338² + 487² + 9397² is the sum of 3 positive squares.
88655022² = 6106878² + 88444440² is the sum of 2 positive squares in 1 way.
88655022² is the sum of 3 positive squares.
88655022 is a proper divisor of 1663¹⁷⁵⁴⁷ - 1.

Number of the day: 4604

Properties of the number 4604:

4604 = 2² × 1151 is the 3980^th composite number and is not squarefree.
4604 has 2 distinct prime factors, 6 divisors, 15 antidivisors and 2300 totatives.
4604 has a semiprime digit sum 14 in base 10.
4604 = 1152² - 1150² is the difference of 2 nonnegative squares in 1 way.
4604 is the difference of 2 positive pentagonal numbers in 1 way.
4604 is not the sum of 3 positive squares.
4604² is the sum of 3 positive squares.
4604 is a proper divisor of 683¹⁰ - 1.
4604 is palindromic in (at least) the following bases: 18, -43, and -59.
4604 in base 17 = ffe and consists of only the digits 'e' and 'f'.
4604 in base 18 = e3e and consists of only the digits '3' and 'e'.

The number 4604 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A004112: Numbers n where |cos(n)| (or |cosec(n)| or |cot(n)|) decreases monotonically to 0; also |tan(n)|, |sec(n)|, |sin(n)| increases.
A046964: Sin(n) decreases monotonically to -1.
A054098: Triangular array generated by its row sums: T(n,0)=1 for n >= 0, T(1,1)=2, T(n,k)=T(n,k-1)+d*r(n-k) for k=2,3,...,n, d=(-1)^(k+1), n >= 2, r(h)=sum of the numbers in row h of T.
A065850: Let u be any string of n digits from {0,...,8}; let f(u) = number of distinct primes, not beginning with 0, formed by permuting the digits of u; then a(n) = max_u f(u).
A066857: Smallest number k such that n! - k is a square
A085329: Non-palindromic solutions to sigma(Rev(n)) = sigma(n).
A139479: Numbers n such that 24n+7 belongs to A000043.
A156167: Numbers n such that n![7]-1 is prime (where n![7] = A114799(n) = septuple factorial).
A220681: T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without consecutive collinear links
A237834: Number of partitions of n such that (greatest part) - (least part) >= number of parts.

Number of the day: 9842

Properties of the number 9842:

9842 = 2 × 7 × 19 × 37 is the 8627^th composite number and is squarefree.
9842 has 4 distinct prime factors, 16 divisors, 21 antidivisors and 3888 totatives.
9842 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 9842 results in a semiprime.
9842 = 4² + 5² + 99² is the sum of 3 positive squares.
9842² = 3192² + 9310² is the sum of 2 positive squares in 1 way.
9842² is the sum of 3 positive squares.
9842 is a proper divisor of 1597⁴ - 1.
9842 = '9' + '842' is the concatenation of 2 semiprime numbers.
9842 is palindromic in (at least) the following bases: 26, 29, 60, -3, -27, -80, and -82.
9842 in base 3 = 111111112 and consists of only the digits '1' and '2'.
9842 in base 24 = h22 and consists of only the digits '2' and 'h'.
9842 in base 26 = eee and consists of only the digit 'e'.
9842 in base 27 = dde and consists of only the digits 'd' and 'e'.
9842 in base 29 = bkb and consists of only the digits 'b' and 'k'.
9842 in base 37 = 770 and consists of only the digits '0' and '7'.
9842 in base 40 = 662 and consists of only the digits '2' and '6'.
9842 in base 49 = 44g and consists of only the digits '4' and 'g'.
9842 in base 59 = 2mm and consists of only the digits '2' and 'm'.
9842 in base 60 = 2i2 and consists of only the digits '2' and 'i'.

The number 9842 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005581: a(n) = (n-1)*n*(n+4)/6.
A007051: a(n) = (3^n + 1)/2.
A047848: Array T read by diagonals; n-th difference of (T(k,n),T(k,n-1),...,T(k,0)) is (k+2)^(n-1), for n=1,2,3,...; k=0,1,2,...
A059934: Third step in Goodstein sequences, i.e. g(5) if g(2)=n: write g(4)=A057650(n) in hereditary representation base 4, bump to base 5, then subtract 1 to produce g(5).
A124302: Number of set partitions with at most 3 blocks; number of Dyck paths of height at most 4; dimension of space of symmetric polynomials in 3 noncommuting variables.
A191450: Dispersion of (3n-1), read by antidiagonals.
A243066: Permutation of natural numbers, the even bisection of A241909 incremented by one and halved; equally, a composition of A241909 and A048673: a(n) = A048673(A241909(n)).
A243506: Permutation of natural numbers: a(n) = A048673(A122111(n)).
A254051: Square array A by downward antidiagonals: A(n,k) = (3 + 3^n*(2*floor(3*k/2) - 1))/6, n,k >= 1; read as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
A278984: Array read by antidiagonals downwards: T(b,n) = number of words of length n over an alphabet of size b that are in standard order.

Number of the day: 81140298

Properties of the number 81140298:

81140298 = 2 × 3 × 19 × 711757 is the 76408061^th composite number and is squarefree.
81140298 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 25623216 totatives.
81140298 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 81140298 results in a sphenic number.
81140298 = 95³ + 308³ + 371³ is the sum of 3 positive cubes in 1 way.
81140298 = 32² + 115² + 9007² is the sum of 3 positive squares.
81140298² = 20903610² + 78401448² is the sum of 2 positive squares in 1 way.
81140298² is the sum of 3 positive squares.
81140298 is a proper divisor of 1291⁴⁶⁵² - 1.

Number of the day: 10956

Properties of the number 10956:

10956 = 2² × 3 × 11 × 83 is the 9625^th composite number and is not squarefree.
10956 has 4 distinct prime factors, 24 divisors, 9 antidivisors and 3280 totatives.
10956 has a semiprime digit sum 21 in base 10.
10956 has a Fibonacci digit sum 21 in base 10.
10956 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 10956 results in a sphenic number.
10956 = 1³ + 16³ + 19³ is the sum of 3 positive cubes in 1 way.
10956 = 2740² - 2738² = 916² - 910² = 260² - 238² = 116² - 50² is the difference of 2 nonnegative squares in 4 ways.
10956 is the sum of 2 positive triangular numbers.
10956 is the difference of 2 positive pentagonal numbers in 1 way.
10956 = 34² + 70² + 70² is the sum of 3 positive squares.
10956² is the sum of 3 positive squares.
10956 is a proper divisor of 331² - 1.
10956 is palindromic in (at least) base -47.
10956 in base 39 = 77a and consists of only the digits '7' and 'a'.
10956 in base 46 = 588 and consists of only the digits '5' and '8'.

The number 10956 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A106455: Sequence A106456 interpreted as binary numbers and converted to decimal.
A111533: Row 6 of table A111528.
A114939: Number of essentially different seating arrangements for n couples around a circular table with 2n seats avoiding spouses being neighbors and avoiding clusters of 3 persons with equal gender.
A123862: Expansion of f(q)*f(q^7)/(f(-q)*f(-q^7)) in powers of q where f() is a Ramanujan theta function.
A133242: Indices n such that A134204(n) < n.
A210860: Triangle of coefficients of polynomials u(n,x) jointly generated with A210861; see the Formula section of A210861.
A213818: Antidiagonal sums of the convolution array A213773.
A232137: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order
A281864: Number of sets of exactly four positive integers <= n having a square element sum.
A289227: Number of ways to select 6 disjoint point triples from an n X n X n triangular point grid, each point triple forming a 2 X 2 X 2 triangle.

Number of the day: 94536

Properties of the number 94536:

94536 = 2³ × 3² × 13 × 101 is the 85419^th composite number and is not squarefree.
94536 has 4 distinct prime factors, 48 divisors, 15 antidivisors and 28800 totatives.
94536 has a triangular digit product 3240 in base 10.
94536 is the difference of 2 nonnegative squares in 12 ways.
94536 is the sum of 2 positive triangular numbers.
94536 is the difference of 2 positive pentagonal numbers in 3 ways.
94536 = 90² + 294² = 30² + 306² is the sum of 2 positive squares in 2 ways.
94536 = 16² + 74² + 298² is the sum of 3 positive squares.
94536² = 52920² + 78336² = 36360² + 87264² = 18360² + 92736² = 18720² + 92664² is the sum of 2 positive squares in 4 ways.
94536² is the sum of 3 positive squares.
94536 is a proper divisor of 1009⁴ - 1.
94536 = '9453' + '6' is the concatenation of 2 triangular numbers.
94536 is palindromic in (at least) the following bases: -57, and -95.
94536 in base 56 = U88 and consists of only the digits '8' and 'U'.

The number 94536 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A012698: E.g.f.: sin(arctanh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+16/4!*x^4-50/5!*x^5...
A012704: arcsinh(arctanh(x)*log(x+1)) = 2/2!*x^2-3/3!*x^3+16/4!*x^4-50/5!*x^5...
A187277: Let S denote the palindromes in the language {0,1,2,...,n-1}*; a(n) = number of words of length 4 in the language SS.
A192770: Numbers n such that n^2 + 1 is divisible by precisely four distinct primes where the sum of the largest and the smallest is equal to the sum of the other two.
A195674: Numbers that are formed using their own digits and addition and seventh power operators.
A199924: Numbers n such that the sum of the largest and the smallest prime divisor of n^2 + 1 equals the sum of the other distinct prime divisors.
A215950: Numbers n > 1 such that the sum of the distinct prime divisors of n^2 + 1 that are congruent to 1 mod 8 equals the sum of the distinct prime divisors congruent to 5 mod 8.

Number of the day: 790843

Properties of the number 790843:

790843 is a cyclic number.
790843 is the 63272^th prime.
790843 has 29 antidivisors and 790842 totatives.
790843 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 790843 results in an emirp.
790843 = 395422² - 395421² is the difference of 2 nonnegative squares in 1 way.
790843 is the sum of 2 positive triangular numbers.
790843 is the difference of 2 positive pentagonal numbers in 1 way.
790843 = 123² + 155² + 867² is the sum of 3 positive squares.
790843² is the sum of 3 positive squares.
790843 is a proper divisor of 1913³⁹ - 1.
790843 is an emirp in (at least) the following bases: 5, 8, 10, 11, 19, 21, 23, 26, 28, 29, 30, 31, 41, 44, 54, 61, 64, 67, 76, 85, 86, 89, 94, 97, 99, and 100.

Number of the day: 7222017

Happy Casual π Day!

Properties of the number 7222017:

7222017 is a cyclic number.
7222017 = 3 × 11 × 218849 is a sphenic number and squarefree.
7222017 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 4376960 totatives.
7222017 has a semiprime digit sum 21 in base 10.
7222017 has a Fibonacci digit sum 21 in base 10.
7222017 has a triangular digit sum 21 in base 10.
7222017 = 3611009² - 3611008² = 1203671² - 1203668² = 328279² - 328268² = 109441² - 109408² is the difference of 2 nonnegative squares in 4 ways.
7222017 is the difference of 2 positive pentagonal numbers in 2 ways.
7222017 = 53² + 218² + 2678² is the sum of 3 positive squares.
7222017² = 3016200² + 6562017² is the sum of 2 positive squares in 1 way.
7222017² is the sum of 3 positive squares.
7222017 is a proper divisor of 397⁶⁸³⁹ - 1.

Number of the day: 1844

Properties of the number 1844:

1844 = 2² × 461 is the 1561^th composite number and is not squarefree.
1844 has 2 distinct prime factors, 6 divisors, 9 antidivisors and 920 totatives.
1844 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 1844 results in a prime.
1844 = 1³ + 8³ + 11³ is the sum of 3 positive cubes in 1 way.
1844 = 462² - 460² is the difference of 2 nonnegative squares in 1 way.
1844 is the difference of 2 positive pentagonal numbers in 1 way.
1844 = 20² + 38² is the sum of 2 positive squares in 1 way.
1844 = 10² + 12² + 40² is the sum of 3 positive squares.
1844² = 1044² + 1520² is the sum of 2 positive squares in 1 way.
1844² is the sum of 3 positive squares.
1844 is a proper divisor of 509⁴ - 1.
1844 is palindromic in (at least) the following bases: 20, -13, -14, -23, and -97.
1844 in base 13 = abb and consists of only the digits 'a' and 'b'.
1844 in base 17 = 668 and consists of only the digits '6' and '8'.
1844 in base 20 = 4c4 and consists of only the digits '4' and 'c'.
1844 in base 42 = 11c and consists of only the digits '1' and 'c'.

The number 1844 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A014561: Numbers n giving rise to prime quadruples (30n+11, 30n+13, 30n+17, 30n+19).
A024026: a(n) = 3^n - n^3.
A067979: Triangle read by rows of incomplete convolutions of Lucas numbers L(n+1) = A000204(n+1), n>=0.
A067990: Triangle A067979 with rows read backwards.
A118551: a(0)=1. a(n) = a(n-1)*2, if n is in the sequence. a(n) = a(n-1) + 1 if n is missing from the sequence.
A134619: Numbers such that the arithmetic mean of the cubes of their prime factors (taken with multiplicity) is a prime.
A138920: Indices k such that A020509(k)=Phi[k](-10) is prime, where Phi is a cyclotomic polynomial.
A138940: Indices n such that A019328(n) = Phi(n,10) is prime, where Phi is a cyclotomic polynomial.
A181470: Numbers n such that 97 is the largest prime factor of n^2-1.
A265067: Coordination sequence for (2,5,8) tiling of hyperbolic plane.

Number of the day: 6052

Properties of the number 6052:

6052 = 2² × 17 × 89 is the 5262^th composite number and is not squarefree.
6052 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 2816 totatives.
6052 has an emirp digit sum 13 in base 10.
6052 has a Fibonacci digit sum 13 in base 10.
Reversing the decimal digits of 6052 results in a sphenic number.
6052 = (53 × 54)/2 + … + (56 × 57)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6052 = 1514² - 1512² = 106² - 72² is the difference of 2 nonnegative squares in 2 ways.
6052 is the difference of 2 positive pentagonal numbers in 1 way.
6052 = 54² + 56² = 24² + 74² is the sum of 2 positive squares in 2 ways.
6052 = 34² + 36² + 60² is the sum of 3 positive squares.
6052² = 2848² + 5340² = 220² + 6048² = 3552² + 4900² = 2652² + 5440² is the sum of 2 positive squares in 4 ways.
6052² is the sum of 3 positive squares.
6052 is a proper divisor of 1123⁴ - 1.
6052 is palindromic in (at least) the following bases: 36, 50, 55, 88, -31, -42, and -55.
6052 in base 6 = 44004 and consists of only the digits '0' and '4'.
6052 in base 27 = 884 and consists of only the digits '4' and '8'.
6052 in base 35 = 4ww and consists of only the digits '4' and 'w'.
6052 in base 36 = 4o4 and consists of only the digits '4' and 'o'.
6052 in base 49 = 2PP and consists of only the digits '2' and 'P'.
6052 in base 50 = 2L2 and consists of only the digits '2' and 'L'.
6052 in base 54 = 244 and consists of only the digits '2' and '4'.
6052 in base 55 = 202 and consists of only the digits '0' and '2'.

The number 6052 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006128: Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n.
A018813: Number of lines through exactly 6 points of an n X n grid of points.
A028305: Triangle of numbers of permutations eliminating just k cards out of n in game of Mousetrap.
A101709: Number of partitions of n having nonnegative even rank (the rank of a partition is the largest part minus the number of parts).
A108099: a(n) = 8n^2 + 8n + 4.
A122919: Inverse of Riordan array (1/(1+x+x^2),x/(1+x)^2).
A237832: Number of partitions of n such that (greatest part) - (least part) = number of parts.
A244385: Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + ... + n^37 is prime.
A272423: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 473", based on the 5-celled von Neumann neighborhood.
A277449: Numbers n such that there is exactly one nontrivial square n-gonal number.

Number of the day: 4274

Properties of the number 4274:

4274 = 2 × 2137 is semiprime and squarefree.
4274 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 2136 totatives.
4274 has an emirp digit sum 17 in base 10.
4274 has sum of divisors equal to 6414 which is a sphenic number.
4274 = 7² + 65² is the sum of 2 positive squares in 1 way.
4274 = 15² + 32² + 55² is the sum of 3 positive squares.
4274² = 910² + 4176² is the sum of 2 positive squares in 1 way.
4274² is the sum of 3 positive squares.
4274 is a proper divisor of 263⁸⁹ - 1.
4274 = '4' + '274' is the concatenation of 2 semiprime numbers.
4274 is an emirpimes in (at least) the following bases: 3, 4, 13, 14, 16, 17, 25, 27, 28, 29, 31, 34, 35, 36, 38, 39, 44, 45, 52, 56, 57, 61, 64, 68, 69, 70, 73, 75, 80, 87, 89, 91, 94, 97, and 99.
4274 is palindromic in (at least) the following bases: -35, and -48.

The number 4274 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007498: Unique period lengths of primes mentioned in A007615.
A051627: Periods associated with A040017.
A125754: Numbers n whose reverse binary representation has the following property: let a 0 mean "halving" and a 1 mean "k -> 3k+1". The number describes an operation k -> f_n(k). If the equation f_n(k) = k has an integer solution, n is a term in the sequence.
A125756: Numbers n whose reverse binary representation has the following property: let a 0 mean "halving" and a 1 mean "k -> 3k+1". The number describes an operation k -> f_n(k). If the equation f_n(k) = k has a positive integer solution, n is a term in the sequence.
A138940: Indices n such that A019328(n) = Phi(n,10) is prime, where Phi is a cyclotomic polynomial.
A201077: G.f.: 1 / Product_{i>=1} (1-q^(2*i-1))^2*(1-q^(12*i-8))*(1-q^(12*i-6))*(1-q^(12*i-4))*(1-q^(12*i)).
A217891: T(n,k)=Number of n element 1..n arrays with each element the minimum of k adjacent elements of a permutation of 1..n+k-1 of n+k-1 elements
A267167: Growth series for affine Coxeter group B_4.
A275188: Positions of 8 in A274640.
A278784: Numbers n such that A000041(n) is of the form 2^7 * k for odd k.

Number of the day: 3045

Properties of the number 3045:

3045 = 3 × 5 × 7 × 29 is the 2608^th composite number and is squarefree.
3045 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 1344 totatives.
3045 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 3045 results in a semiprime.
3045 = 1523² - 1522² = 509² - 506² = 307² - 302² = 221² - 214² = 109² - 94² = 83² - 62² = 67² - 38² = 61² - 26² is the difference of 2 nonnegative squares in 8 ways.
3045 is the sum of 2 positive triangular numbers.
3045 is the difference of 2 positive pentagonal numbers in 3 ways.
3045 = 20² + 23² + 46² is the sum of 3 positive squares.
3045² = 2100² + 2205² = 357² + 3024² = 504² + 3003² = 1827² + 2436² is the sum of 2 positive squares in 4 ways.
3045² is the sum of 3 positive squares.
3045 is a proper divisor of 349² - 1.
3045 is palindromic in (at least) base 86.
3045 in base 12 = 1919 and consists of only the digits '1' and '9'.
3045 in base 14 = 1177 and consists of only the digits '1' and '7'.
3045 in base 19 = 885 and consists of only the digits '5' and '8'.
3045 in base 22 = 669 and consists of only the digits '6' and '9'.
3045 in base 27 = 44l and consists of only the digits '4' and 'l'.

The number 3045 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000266: E.g.f. exp(-x^2/2) / (1-x).
A005476: a(n) = n*(5*n - 1)/2.
A007059: Number of balanced ordered trees with n nodes.
A022289: a(n) = n*(31*n + 1)/2.
A024966: 7 times triangular numbers: 7n(n+1)/2.
A034828: a(n) = [n^2/4]*n/2.
A055561: Numbers n such that there are precisely 3 groups of order n.
A079500: Number of compositions of the integer n in which the first part is >= the other parts.
A094416: Array read by antidiagonals: generalized ordered Bell numbers Bo(r,n).
A128396: Numbers n such that n^2 divides 16^n-1.

Number of the day: 7172017

Happy Yellow Pig Day!

Properties of the number 7172017:

7172017 is a cyclic number.
7172017 = 1877 × 3821 is semiprime and squarefree.
7172017 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 7166320 totatives.
7172017 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 7172017 results in a sphenic number.
7172017 = 3586009² - 3586008² = 2849² - 972² is the difference of 2 nonnegative squares in 2 ways.
7172017 is the sum of 2 positive triangular numbers.
7172017 is the difference of 2 positive pentagonal numbers in 1 way.
7172017 = 1264² + 2361² = 444² + 2641² is the sum of 2 positive squares in 2 ways.
7172017 = 86² + 189² + 2670² is the sum of 3 positive squares.
7172017² = 4386508² + 5674185² = 3976625² + 5968608² = 2345208² + 6777745² = 2289940² + 6796617² is the sum of 2 positive squares in 4 ways.
7172017² is the sum of 3 positive squares.
7172017 is a proper divisor of 137⁷⁶⁴ - 1.
7172017 is an emirpimes in (at least) the following bases: 2, 8, 13, 19, 21, 22, 25, 26, 27, 31, 34, 35, 37, 38, 39, 44, 45, 51, 53, 59, 61, 67, 73, 75, 77, 80, 82, 83, 85, 87, 89, 91, 93, and 97.

Number of the day: 81813

Properties of the number 81813:

81813 = 3 × 27271 is semiprime and squarefree.
81813 has 2 distinct prime factors, 4 divisors, 33 antidivisors and 54540 totatives.
81813 has a semiprime digit sum 21 in base 10.
81813 has a Fibonacci digit sum 21 in base 10.
81813 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 81813 results in a sphenic number.
81813 = 40907² - 40906² = 13637² - 13634² is the difference of 2 nonnegative squares in 2 ways.
81813 is the sum of 2 positive triangular numbers.
81813 is the difference of 2 positive pentagonal numbers in 1 way.
81813 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
81813 = 1² + 4² + 286² is the sum of 3 positive squares.
81813² is the sum of 3 positive squares.
81813 is a proper divisor of 1901⁵⁴ - 1.
81813 is an emirpimes in (at least) the following bases: 3, 6, 7, 9, 15, 19, 33, 35, 48, 51, 55, 61, 67, 71, 78, 81, 85, and 99.
81813 is palindromic in (at least) base -55.
81813 in base 54 = S33 and consists of only the digits '3' and 'S'.

The number 81813 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A053948: Numbers n such that n^2 contains only digits {3,6,9}.
A137041: Numbers n such that n and the square of n use only the digits 1, 3, 6, 8 and 9.

Number of the day: 3509167

Properties of the number 3509167:

3509167 is a cyclic number.
3509167 = 19 × 184693 is semiprime and squarefree.
3509167 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 3324456 totatives.
3509167 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 3509167 results in a sphenic number.
3509167 = 1754584² - 1754583² = 92356² - 92337² is the difference of 2 nonnegative squares in 2 ways.
3509167 is the sum of 2 positive triangular numbers.
3509167 is the difference of 2 positive pentagonal numbers in 2 ways.
3509167 is not the sum of 3 positive squares.
3509167² = 2134308² + 2785495² is the sum of 2 positive squares in 1 way.
3509167² is the sum of 3 positive squares.
3509167 is a proper divisor of 37³⁰⁷⁸² - 1.
3509167 is an emirpimes in (at least) the following bases: 4, 6, 11, 13, 24, 25, 26, 31, 38, 42, 43, 44, 45, 47, 53, 55, 58, 64, 71, 76, 81, 83, 86, 87, 93, 95, 99, and 100.

The number 3509167 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A159339: Transform of A056594 by the T_{1,0} transformation (see link)

Number of the day: 96063

Properties of the number 96063:

96063 is a cyclic number.
96063 = 3 × 11 × 41 × 71 is the 86804^th composite number and is squarefree.
96063 has 4 distinct prime factors, 16 divisors, 31 antidivisors and 56000 totatives.
Reversing the decimal digits of 96063 results in a sphenic number.
96063 = 48032² - 48031² = 16012² - 16009² = 4372² - 4361² = 1472² - 1439² = 1192² - 1151² = 712² - 641² = 452² - 329² = 332² - 119² is the difference of 2 nonnegative squares in 8 ways.
96063 is the sum of 2 positive triangular numbers.
96063 is the difference of 2 positive pentagonal numbers in 4 ways.
96063 is not the sum of 3 positive squares.
96063² = 21087² + 93720² is the sum of 2 positive squares in 1 way.
96063² is the sum of 3 positive squares.
96063 is a proper divisor of 283¹⁰ - 1.
96063 is palindromic in (at least) the following bases: 85, and -62.
96063 in base 61 = Pnn and consists of only the digits 'P' and 'n'.

The number 96063 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A115132: Partial sums of A064059.
A123789: Number of ways, counted up to symmetry, to build a contiguous building with n LEGO blocks of size 1x5 which is flat, i.e. with all blocks in parallel position and symmetric after a rotation by 180 degrees.

Number of the day: 378349

Properties of the number 378349:

378349 is a cyclic number.
378349 = 67 × 5647 is semiprime and squarefree.
378349 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 372636 totatives.
378349 has a semiprime digit sum 34 in base 10.
378349 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 378349 results in an emirpimes.
378349 = (71 × 72)/2 + … + (137 × 138)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
378349 = 189175² - 189174² = 2857² - 2790² is the difference of 2 nonnegative squares in 2 ways.
378349 is the sum of 2 positive triangular numbers.
378349 is the difference of 2 positive pentagonal numbers in 2 ways.
378349 = 72² + 77² + 606² is the sum of 3 positive squares.
378349² is the sum of 3 positive squares.
378349 is a proper divisor of 853³³ - 1.
378349 = '37834' + '9' is the concatenation of 2 semiprime numbers.
378349 is an emirpimes in (at least) the following bases: 2, 10, 11, 12, 16, 18, 26, 27, 28, 32, 34, 42, 43, 45, 46, 47, 51, 55, 58, 60, 62, 63, 64, 65, 67, 69, 70, 71, 73, 75, 83, 91, 93, 94, 96, 97, and 100.
378349 is palindromic in (at least) base -92.

Number of the day: 1437

Properties of the number 1437:

1437 is a cyclic number.
1437 = 3 × 479 is semiprime and squarefree.
1437 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 956 totatives.
1437 has an emirpimes digit sum 15 in base 10.
1437 has a triangular digit sum 15 in base 10.
Reversing the decimal digits of 1437 results in an emirpimes.
1437 = 719² - 718² = 241² - 238² is the difference of 2 nonnegative squares in 2 ways.
1437 is the sum of 2 positive triangular numbers.
1437 is the difference of 2 positive pentagonal numbers in 1 way.
1437 = 5² + 16² + 34² is the sum of 3 positive squares.
1437² is the sum of 3 positive squares.
1437 is a proper divisor of 7²³⁹ - 1.
1437 is an emirpimes in (at least) the following bases: 3, 4, 10, 11, 19, 20, 23, 29, 30, 33, 34, 35, 36, 37, 43, 45, 46, 47, 48, 49, 55, 59, 60, 63, 66, 67, 68, 69, 71, 73, 79, 82, 92, 93, and 99.
1437 is palindromic in (at least) the following bases: 12, and -35.
1437 in base 5 = 21222 and consists of only the digits '1' and '2'.
1437 in base 12 = 9b9 and consists of only the digits '9' and 'b'.
1437 in base 37 = 11V and consists of only the digits '1' and 'V'.

The number 1437 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003037: Smallest number of complexity n: smallest number requiring n 1's to build using +, * and ^.
A032523: Index of first occurrence of n as a term in A001203, the continued fraction for Pi.
A051227: Bernoulli number B_{2n} has denominator 42.
A103471: Number of polyominoes without holes consisting of 5 regular unit n-gons.
A123142: Number of benzenoids with 23 hexagons, C_(2v) symmetry and containing n carbon atoms.
A124178: Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 is prime.
A191723: Dispersion of A047215, (numbers >1 and congruent to 0 or 2 mod 5), by antidiagonals.
A204867: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly two different ways, and new values 0..1 introduced in row major order
A219852: T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nXk array
A250167: T(n,k)=Number of length n+1 0..k arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero

Number of the day: 21846217

Properties of the number 21846217:

21846217 is a cyclic number.
21846217 = 1621 × 13477 is semiprime and squarefree.
21846217 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 21831120 totatives.
21846217 has an emirp digit sum 31 in base 10.
21846217 = 10923109² - 10923108² = 7549² - 5928² is the difference of 2 nonnegative squares in 2 ways.
21846217 is the sum of 2 positive triangular numbers.
21846217 is the difference of 2 positive pentagonal numbers in 2 ways.
21846217 = 2436² + 3989² = 216² + 4669² is the sum of 2 positive squares in 2 ways.
21846217 = 142² + 303² + 4662² is the sum of 3 positive squares.
21846217² = 10512060² + 19150817² = 9978025² + 19434408² = 2017008² + 21752905² = 12235308² + 18098465² is the sum of 2 positive squares in 4 ways.
21846217² is the sum of 3 positive squares.
21846217 is a proper divisor of 433¹⁰¹⁰⁷ - 1.
21846217 = '218' + '46217' is the concatenation of 2 semiprime numbers.
21846217 is an emirpimes in (at least) the following bases: 7, 9, 12, 14, 16, 18, 19, 29, 33, 34, 35, 38, 43, 45, 47, 50, 52, 53, 54, 61, 64, 66, 67, 73, 74, 77, 78, 82, 83, 90, 91, 97, 99, and 100.

Number of the day: 399301

Properties of the number 399301:

399301 = 7² × 29 × 281 is the 365494^th composite number and is not squarefree.
399301 has 3 distinct prime factors, 12 divisors, 19 antidivisors and 329280 totatives.
399301 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 399301 results in a prime.
399301 = 199651² - 199650² = 28525² - 28518² = 6899² - 6870² = 4099² - 4050² = 1085² - 882² = 851² - 570² is the difference of 2 nonnegative squares in 6 ways.
399301 is the sum of 2 positive triangular numbers.
399301 is the difference of 2 positive pentagonal numbers in 5 ways.
399301 = 399² + 490² = 49² + 630² is the sum of 2 positive squares in 2 ways.
399301 = 81² + 104² + 618² is the sum of 3 positive squares.
399301² = 227360² + 328251² = 80899² + 391020² = 61740² + 394499² = 275380² + 289149² is the sum of 2 positive squares in 4 ways.
399301² is the sum of 3 positive squares.
399301 is a proper divisor of 181¹⁴ - 1.
399301 = '39' + '9301' is the concatenation of 2 semiprime numbers.
399301 is palindromic in (at least) base -85.

The number 399301 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A230759: Values of x such that x^2 + y^2 = 53^n with x and y coprime and 0 < x < y.

Number of the day: 849956

Properties of the number 849956:

849956 = 2² × 103 × 2063 is the 782342^th composite number and is not squarefree.
849956 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 420648 totatives.
849956 has a prime digit sum 41 in base 10.
849956 = 212490² - 212488² = 2166² - 1960² is the difference of 2 nonnegative squares in 2 ways.
849956 is the difference of 2 positive pentagonal numbers in 1 way.
849956 = 34² + 156² + 908² is the sum of 3 positive squares.
849956² is the sum of 3 positive squares.
849956 is a proper divisor of 1237¹⁰³¹ - 1.
849956 in base 47 = 88a8 and consists of only the digits '8' and 'a'.

Number of the day: 62542

Properties of the number 62542:

62542 = 2 × 31271 is semiprime and squarefree.
62542 has 2 distinct prime factors, 4 divisors, 21 antidivisors and 31270 totatives.
62542 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 62542 results in an emirpimes.
62542 is the sum of 2 positive triangular numbers.
62542 is the difference of 2 positive pentagonal numbers in 2 ways.
62542 = 10² + 21² + 249² is the sum of 3 positive squares.
62542² is the sum of 3 positive squares.
62542 is a proper divisor of 101¹⁰⁶ - 1.
62542 = '62' + '542' is the concatenation of 2 semiprime numbers.
62542 is an emirpimes in (at least) the following bases: 5, 6, 10, 14, 15, 16, 19, 20, 22, 26, 28, 29, 32, 35, 36, 40, 43, 53, 54, 56, 59, 64, 67, 68, 71, 73, 74, 76, 77, 82, 83, 85, 86, 87, and 90.
62542 is palindromic in (at least) the following bases: 58, -61, -74, and -81.
62542 in base 23 = 5355 and consists of only the digits '3' and '5'.
62542 in base 58 = IYI and consists of only the digits 'I' and 'Y'.
62542 in base 60 = HMM and consists of only the digits 'H' and 'M'.
62542 in base 62 = GGk and consists of only the digits 'G' and 'k'.

Number of the day: 9357

Properties of the number 9357:

9357 is a cyclic number.
9357 = 3 × 3119 is semiprime and squarefree.
9357 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 6236 totatives.
Reversing the decimal digits of 9357 results in a sphenic number.
9357 = 4679² - 4678² = 1561² - 1558² is the difference of 2 nonnegative squares in 2 ways.
9357 is the difference of 2 positive pentagonal numbers in 1 way.
9357 = 11² + 20² + 94² is the sum of 3 positive squares.
9357² is the sum of 3 positive squares.
9357 is a proper divisor of 13¹⁵⁵⁹ - 1.
9357 = '93' + '57' is the concatenation of 2 semiprime numbers.
9357 is an emirpimes in (at least) the following bases: 2, 3, 6, 9, 11, 22, 25, 27, 28, 32, 36, 42, 50, 51, 54, 55, 57, 59, 60, 67, 74, 78, 87, 89, 93, 97, 98, 99, and 100.
9357 is palindromic in (at least) base 47.
9357 in base 22 = j77 and consists of only the digits '7' and 'j'.
9357 in base 36 = 77x and consists of only the digits '7' and 'x'.
9357 in base 46 = 4JJ and consists of only the digits '4' and 'J'.
9357 in base 47 = 4B4 and consists of only the digits '4' and 'B'.

The number 9357 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A050969: Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 20.
A076623: Total number of left truncatable primes (without zeros) in base n.
A114615: Starting numbers for which the RATS sequence has eventual period 14.
A138990: a(n) = Frobenius number for 4 successive primes = F[p(n),p(n+1),p(n+2),p(n+3)].
A142462: Triangle read by rows: T(n,k) (1<=k<=n) given by T(n, 1) = T(n,n) = 1, otherwise T(n, k) = (m*n-m*k+1)*T(n-1,k-1)+(m*k-m+1)*T(n-1,k), where m = 7.
A155121: 2*n*(1+n+n^2+n^3)-3.
A182708: a(n)=A046746(n)-A000041(n-1). Sum of the smallest parts of all partitions of n that do not contain 1 as a part.
A224956: Number of partitions of n where the difference between consecutive parts is at most 2.
A238553: Numbers n such that the decimal expansions of both n and n^2 have 3 as the digit with the smallest value and 9 as the digit with the largest value.
A262508: Numbers that occur only once in A155043; positions of zeros in A262505, ones in A262507.

Number of the day: 991735

Properties of the number 991735:

991735 is a cyclic number.
991735 = 5 × 198347 is semiprime and squarefree.
991735 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 793384 totatives.
991735 has a semiprime digit sum 34 in base 10.
991735 has a Fibonacci digit sum 34 in base 10.
991735 = 495868² - 495867² = 99176² - 99171² is the difference of 2 nonnegative squares in 2 ways.
991735 is the difference of 2 positive pentagonal numbers in 2 ways.
991735 is not the sum of 3 positive squares.
991735² = 595041² + 793388² is the sum of 2 positive squares in 1 way.
991735² is the sum of 3 positive squares.
991735 is a proper divisor of 11⁹⁹¹⁷³ - 1.
991735 = '99173' + '5' is the concatenation of 2 prime numbers.
991735 = '9917' + '35' is the concatenation of 2 semiprime numbers.
991735 is an emirpimes in (at least) the following bases: 5, 8, 13, 15, 17, 20, 23, 28, 34, 35, 37, 39, 53, 56, 57, 59, 61, 65, 70, 71, 79, 80, 83, 85, 87, 88, 90, and 98.

Number of the day: 639918

Properties of the number 639918:

639918 = 2 × 3² × 73 × 487 is the 587849^th composite number and is not squarefree.
639918 has 4 distinct prime factors, 24 divisors, 29 antidivisors and 209952 totatives.
639918 has a triangular digit sum 36 in base 10.
639918 is the sum of 2 positive triangular numbers.
639918 = 62² + 85² + 793² is the sum of 3 positive squares.
639918² = 420768² + 482130² is the sum of 2 positive squares in 1 way.
639918² is the sum of 3 positive squares.
639918 is a proper divisor of 41¹⁸ - 1.

Number of the day: 6728971752

Properties of the number 6728971752:

6728971752 = 2³ × 3³ × 19 × 1639613 is the 6417133092^th composite number and is not squarefree.
6728971752 has 4 distinct prime factors, 64 divisors, 19 antidivisors and 2124937152 totatives.
6728971752 = 852³ + 1178³ + 1648³ = 180³ + 1178³ + 1720³ is the sum of 3 positive cubes in 2 ways.
6728971752 is the difference of 2 nonnegative squares in 16 ways.
6728971752 is the difference of 2 positive pentagonal numbers in 4 ways.
6728971752 = 26² + 224² + 82030² is the sum of 3 positive squares.
6728971752² = 3900749400² + 5482993248² is the sum of 2 positive squares in 1 way.
6728971752² is the sum of 3 positive squares.
6728971752 is a proper divisor of 1747¹⁸⁹¹⁸⁶ - 1.

Number of the day: 890905

Gottfried Wilhelm Leibniz was born on this day 371 years ago.

Properties of the number 890905:

890905 = 5 × 23 × 61 × 127 is the 820289^th composite number and is squarefree.
890905 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 665280 totatives.
890905 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 890905 results in a sphenic number.
890905 = 445453² - 445452² = 89093² - 89088² = 19379² - 19356² = 7333² - 7272² = 3931² - 3816² = 3571² - 3444² = 1613² - 1308² = 1019² - 384² is the difference of 2 nonnegative squares in 8 ways.
890905 is the difference of 2 positive pentagonal numbers in 7 ways.
890905 = 25² + 54² + 942² is the sum of 3 positive squares.
890905² = 397256² + 797433² = 160655² + 876300² = 604647² + 654304² = 534543² + 712724² is the sum of 2 positive squares in 4 ways.
890905² is the sum of 3 positive squares.
890905 is a proper divisor of 1289⁶⁰ - 1.
890905 is palindromic in (at least) base -56.