Number of the day: 571682

Properties of the number 571682:

571682 = 2 × 285841 is semiprime and squarefree.
571682 has 2 distinct prime factors, 4 divisors, 21 antidivisors and 285840 totatives.
571682 has a prime digit sum 29 in base 10.
571682 = 401² + 641² is the sum of 2 positive squares in 1 way.
571682 = 19² + 36² + 755² is the sum of 3 positive squares.
571682² = 250080² + 514082² is the sum of 2 positive squares in 1 way.
571682² is the sum of 3 positive squares.
571682 is a proper divisor of 277¹⁸ - 1.
571682 is an emirpimes in (at least) the following bases: 2, 6, 8, 11, 13, 15, 23, 24, 25, 28, 34, 43, 44, 54, 55, 61, 63, 64, 65, 66, 69, 80, 82, 84, 91, 95, 96, and 99.
571682 is palindromic in (at least) base -97.

Number of the day: 32139

Properties of the number 32139:

32139 = 3² × 3571 is the 28691^th composite number and is not squarefree.
32139 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 21420 totatives.
32139 = 16070² - 16069² = 5358² - 5355² = 1790² - 1781² is the difference of 2 nonnegative squares in 3 ways.
32139 is the difference of 2 positive pentagonal numbers in 1 way.
32139 = 17² + 35² + 175² is the sum of 3 positive squares.
32139² is the sum of 3 positive squares.
32139 is a proper divisor of 103³ - 1.
32139 = '321' + '39' is the concatenation of 2 emirpimes.
32139 is palindromic in (at least) the following bases: 37, -33, -43, and -63.
32139 in base 34 = rr9 and consists of only the digits '9' and 'r'.
32139 in base 37 = NHN and consists of only the digits 'H' and 'N'.
32139 in base 42 = I99 and consists of only the digits '9' and 'I'.

The number 32139 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A004932: Floor of n*phi^17, where phi is the golden ratio, A001622.
A004952: Nearest integer to n*phi^17, where phi is the golden ratio, A001622.
A114613: Starting numbers for which the RATS sequence has eventual period 3.
A224749: Vauban's sequence: a(n)=0 if n<=0, a(1)=1; thereafter a(n) = 3*a(n-1) + 6*a(n-2) + 6*a(n-3) + 6*a(n-4) + 6*a(n-5).
A251310: Number of (n+1) X (1+1) 0..1 arrays with no 2 X 2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements.
A288492: Indices of terms of A288349 that are powers of 2.

Number of the day: 294229

Properties of the number 294229:

294229 = 13² × 1741 is the 268676^th composite number and is not squarefree.
294229 has 2 distinct prime factors, 6 divisors, 13 antidivisors and 271440 totatives.
294229 has a triangular digit sum 28 in base 10.
294229 = 147115² - 147114² = 11323² - 11310² = 955² - 786² is the difference of 2 nonnegative squares in 3 ways.
294229 is the difference of 2 positive pentagonal numbers in 3 ways.
294229 = 215² + 498² = 198² + 505² = 377² + 390² is the sum of 2 positive squares in 3 ways.
294229 = 105² + 152² + 510² is the sum of 3 positive squares.
294229² = 113165² + 271596² = 103896² + 275275² = 122304² + 267605² = 9971² + 294060² = 207179² + 208920² = 199980² + 215821² = 201779² + 214140² is the sum of 2 positive squares in 7 ways.
294229² is the sum of 3 positive squares.
294229 is a proper divisor of 59¹⁵⁶ - 1.
294229 = '2' + '94229' is the concatenation of 2 prime numbers.
294229 is palindromic in (at least) base 100.

Number of the day: 1087

Properties of the number 1087:

1087 is a cyclic number.
1087 is the 181^th prime.
1087 has 13 antidivisors and 1086 totatives.
Reversing the decimal digits of 1087 results in a semiprime.
1087 = 544² - 543² is the difference of 2 nonnegative squares in 1 way.
1087 is the sum of 2 positive triangular numbers.
1087 is the difference of 2 positive pentagonal numbers in 1 way.
1087 is not the sum of 3 positive squares.
1087² is the sum of 3 positive squares.
1087 is a proper divisor of 257³ - 1.
1087 = '10' + '87' is the concatenation of 2 semiprime numbers.
1087 is an emirp in (at least) the following bases: 2, 6, 13, 14, 15, 17, 19, 21, 25, 28, 29, 30, 34, 35, 37, 40, 41, 42, 43, 49, 50, 53, 56, 59, 61, 62, 67, 73, 75, 81, 83, 92, 94, 95, 97, and 99.
1087 is palindromic in (at least) the following bases: 12, -11, and -31.
1087 in base 12 = 767 and consists of only the digits '6' and '7'.
1087 in base 32 = 11v and consists of only the digits '1' and 'v'.

The number 1087 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006450: Prime-indexed primes: primes with prime subscripts.
A007522: Primes of the form 8n+7, that is, primes congruent to -1 mod 8.
A008483: Number of partitions of n into parts >= 3.
A008865: a(n) = n^2 - 2.
A022005: Initial members of prime triples (p, p+4, p+6).
A023200: Primes p such that p + 4 is also prime.
A107132: Primes of the form 2x^2 + 13y^2.
A139643: Primes of the form x^2+Ny^2, with N=102.
A140633: Primes of the form 7x^2+4xy+52y^2.
A235482: Primes whose base-5 representation is also the base-9 representation of a prime.

Number of the day: 651

Properties of the number 651:

651 = 3 × 7 × 31 is a sphenic number and squarefree.
651 has 3 distinct prime factors, 8 divisors, 7 antidivisors and 360 totatives.
651 has an oblong digit sum 12 in base 10.
651 has a sphenic digit product 30 in base 10.
651 has an oblong digit product 30 in base 10.
Reversing the decimal digits of 651 results in an oblong number.
651 = (10 × 11)/2 + … + (16 × 17)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
651 = 326² - 325² = 110² - 107² = 50² - 43² = 26² - 5² is the difference of 2 nonnegative squares in 4 ways.
651 is the sum of 2 positive triangular numbers.
651 is the difference of 2 positive pentagonal numbers in 1 way.
651 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
651 = (21 × (3 × 21-1))/2 is a pentagonal number.
651 = 1² + 5² + 25² is the sum of 3 positive squares.
651² is the sum of 3 positive squares.
651 is a proper divisor of 433² - 1.
651 = '6' + '51' is the concatenation of 2 semiprime numbers.
651 is palindromic in (at least) the following bases: 5, 6, 25, 30, 92, -4, -5, -26, -50, and -65.
651 in base 5 = 10101 and consists of only the digits '0' and '1'.
651 in base 6 = 3003 and consists of only the digits '0' and '3'.
651 in base 24 = 133 and consists of only the digits '1' and '3'.
651 in base 25 = 111 and consists of only the digit '1'.

The number 651 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000326: Pentagonal numbers: a(n) = n*(3*n-1)/2.
A001106: 9-gonal (or enneagonal or nonagonal) numbers: a(n) = n*(7*n-5)/2.
A001157: sigma_2(n): sum of squares of divisors of n.
A001318: Generalized pentagonal numbers: m*(3*m - 1)/2, m = 0, +-1, +-2, +-3, ....
A002061: Central polygonal numbers: a(n) = n^2 - n + 1.
A005728: Number of fractions in Farey series of order n.
A006095: Gaussian binomial coefficient [n,2] for q=2.
A022166: Triangle of Gaussian binomial coefficients (or q-binomial coefficients) [n,k] for q = 2.
A027441: a(n) = (n^4 + n)/2, (Row sums of an n X n X n magic cube, when it exists).
A139250: Toothpick sequence (see Comments lines for definition).

Number of the day: 6593

Christiaan Huygens was born on this day 392 years ago.

Properties of the number 6593:

6593 is a cyclic number.
6593 = 19 × 347 is semiprime and squarefree.
6593 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 6228 totatives.
6593 has a prime digit sum 23 in base 10.
6593 = 3297² - 3296² = 183² - 164² is the difference of 2 nonnegative squares in 2 ways.
6593 is the difference of 2 positive pentagonal numbers in 2 ways.
6593 = 7² + 12² + 80² is the sum of 3 positive squares.
6593² is the sum of 3 positive squares.
6593 is a proper divisor of 229¹⁷³ - 1.
6593 = '659' + '3' is the concatenation of 2 prime numbers.
6593 = '65' + '93' is the concatenation of 2 semiprime numbers.
6593 is an emirpimes in (at least) the following bases: 3, 4, 8, 9, 16, 21, 26, 29, 30, 31, 32, 34, 37, 51, 54, 55, 57, 61, 62, 68, 71, 72, 78, 80, 87, 89, 95, and 100.
6593 is palindromic in (at least) the following bases: 6, 36, 64, and -6.
6593 in base 22 = ddf and consists of only the digits 'd' and 'f'.
6593 in base 35 = 5dd and consists of only the digits '5' and 'd'.
6593 in base 36 = 535 and consists of only the digits '3' and '5'.
6593 in base 40 = 44X and consists of only the digits '4' and 'X'.

The number 6593 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A039515: Conjecturally, largest attractor in '3x+(2n+1)' problem.
A047986: Integers n such that A047988(n)=3.
A062725: Write 0,1,2,3,4,... in a triangular spiral, then a(n) is the sequence found by reading the terms along the line from 0 in the direction 0,7,...
A068059: Partial sums of A068058 + 1.
A073592: Euler transform of negative integers.
A074340: a(1) = 5; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A100294: Numbers of the form a^5 + b^4 with a, b > 0.
A105728: Triangle read by rows: T(n,1) = 1, T(n,n) = n and for 1 < k < n: T(n,k) = T(n-1,k-1) + 2*T(n-1,k).
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.
A246325: Total number of ON cells at stage 2n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 453".

Number of the day: 8009

Kari Onni Uolevi Karhunen was born on this day 106 years ago.

Properties of the number 8009:

8009 is a cyclic number.
8009 and 8011 form a twin prime pair.
8009 has 9 antidivisors and 8008 totatives.
8009 has an emirp digit sum 17 in base 10.
8009 has sum of divisors equal to 8010 which is an oblong number.
8009 = 1³ + 2³ + 20³ is the sum of 3 positive cubes in 1 way.
8009 = 4005² - 4004² is the difference of 2 nonnegative squares in 1 way.
8009 is the difference of 2 positive pentagonal numbers in 1 way.
8009 = 28² + 85² is the sum of 2 positive squares in 1 way.
8009 = 17² + 18² + 86² is the sum of 3 positive squares.
8009² = 4760² + 6441² is the sum of 2 positive squares in 1 way.
8009² is the sum of 3 positive squares.
8009 is a proper divisor of 283⁴ - 1.
8009 is an emirp in (at least) the following bases: 2, 4, 11, 18, 23, 26, 29, 31, 35, 38, 41, 46, 49, 50, 63, 65, 67, 71, 76, 81, 84, 85, 87, 89, 91, 92, 93, 94, 96, 97, and 98.
8009 is palindromic in (at least) the following bases: 77, 88, and -91.
8009 in base 36 = 66h and consists of only the digits '6' and 'h'.

The number 8009 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002327: Primes of form n^2 - n - 1.
A033274: Primes that do not contain any other prime as a proper substring.
A045714: Primes with first digit 8.
A069675: Primes with either no internal digits or all internal digits are 0.
A081762: Primes p such that p*(p-2) divides 2^(p-1)-1.
A082108: a(n) = 4n^2 + 6n + 1.
A089392: Magnanimous primes: primes with the property that inserting a "+" in any place between two digits yields a sum which is prime.
A136065: Mother primes of order 6.
A247981: Primes dividing nonzero terms in A003095: the iterates of x^2 + 1 starting at 0.
A260147: G.f.: (1/2) * Sum_{n=-oo..+oo} x^n * (1 + x^n)^n, an even function.

Number of the day: 36507377

Properties of the number 36507377:

36507377 is a cyclic number.
36507377 = 139 × 262643 is semiprime and squarefree.
36507377 has 2 distinct prime factors, 4 divisors, 31 antidivisors and 36244596 totatives.
36507377 has a semiprime digit sum 38 in base 10.
Reversing the decimal digits of 36507377 results in a prime.
36507377 = 18253689² - 18253688² = 131391² - 131252² is the difference of 2 nonnegative squares in 2 ways.
36507377 is the sum of 2 positive triangular numbers.
36507377 is the difference of 2 positive pentagonal numbers in 2 ways.
36507377 = 13² + 38² + 6042² is the sum of 3 positive squares.
36507377² is the sum of 3 positive squares.
36507377 is a proper divisor of 557¹³¹³²¹ - 1.
36507377 is an emirpimes in (at least) the following bases: 5, 11, 12, 15, 20, 21, 22, 25, 26, 30, 34, 35, 41, 44, 45, 49, 50, 54, 55, 61, 63, 64, 65, 70, 71, 73, 74, 75, 76, 80, 85, 86, 94, 95, 97, and 99.

Number of the day: 425268

Élie Joseph Cartan was born on this day 152 years ago.

Properties of the number 425268:

425268 = 2² × 3² × 11813 is the 389470^th composite number and is not squarefree.
425268 has 3 distinct prime factors, 18 divisors, 19 antidivisors and 141744 totatives.
425268 = 106318² - 106316² = 35442² - 35436² = 11822² - 11804² is the difference of 2 nonnegative squares in 3 ways.
425268 is the difference of 2 positive pentagonal numbers in 1 way.
425268 = 282² + 588² is the sum of 2 positive squares in 1 way.
425268 = 8² + 10² + 652² is the sum of 3 positive squares.
425268² = 266220² + 331632² is the sum of 2 positive squares in 1 way.
425268² is the sum of 3 positive squares.
425268 is a proper divisor of 181²⁹⁵³ - 1.
425268 is palindromic in (at least) the following bases: 84, and -95.

Number of the day: 213881

Properties of the number 213881:

213881 is a cyclic number.
213881 is the 19116^th prime.
213881 has 15 antidivisors and 213880 totatives.
213881 has a prime digit sum 23 in base 10.
213881 = 106941² - 106940² is the difference of 2 nonnegative squares in 1 way.
213881 is the difference of 2 positive pentagonal numbers in 1 way.
213881 = 284² + 365² is the sum of 2 positive squares in 1 way.
213881 = 16² + 45² + 460² is the sum of 3 positive squares.
213881² = 52569² + 207320² is the sum of 2 positive squares in 1 way.
213881² is the sum of 3 positive squares.
213881 is a proper divisor of 1811²⁰ - 1.
213881 is an emirp in (at least) the following bases: 7, 14, 15, 16, 21, 30, 33, 35, 50, 58, 60, 61, 63, 66, 67, 69, 71, 74, 78, 82, 85, 89, 91, and 97.
213881 is palindromic in (at least) base 72.

The number 213881 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A129908: Quotient of the decimal representation of concatenated twin primes divided by 3.
A129909: Primes that are the quotient of the decimal representation of concatenated twin primes divided by 3.
A244638: In the '3x+1' problem, primes which as starting values set new records for number of steps to reach 1, where a step means either 'divide by two' or 'triple plus one and then divide by two'.

Number of the day: 1244

Properties of the number 1244:

1244 = 2² × 311 is the 1040^th composite number and is not squarefree.
1244 has 2 distinct prime factors, 6 divisors, 5 antidivisors and 620 totatives.
1244 has a prime digit sum 11 in base 10.
Reversing the decimal digits of 1244 results in a prime.
1244 = 312² - 310² is the difference of 2 nonnegative squares in 1 way.
1244 is the difference of 2 positive pentagonal numbers in 1 way.
1244 is not the sum of 3 positive squares.
1244² is the sum of 3 positive squares.
1244 is a proper divisor of 1867² - 1.
1244 is palindromic in (at least) the following bases: 12, 23, -20, and -27.
1244 in base 12 = 878 and consists of only the digits '7' and '8'.
1244 in base 22 = 2cc and consists of only the digits '2' and 'c'.
1244 in base 23 = 282 and consists of only the digits '2' and '8'.

The number 1244 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000025: Coefficients of the 3rd order mock theta function f(q).
A001749: Primes multiplied by 4.
A003368: Numbers that are the sum of 12 positive 6th powers.
A051226: Numbers m such that the Bernoulli number B_m has denominator 30.
A076042: a(0) = 0; thereafter a(n) = a(n-1) + n^2 if a(n-1) < n^2, otherwise a(n) = a(n-1) - n^2.
A085438: a(n) = Sum_{i=1..n} binomial(i+1,2)^3.
A098743: Number of partitions of n into aliquant parts (i.e., parts that do not divide n).
A126796: Number of complete partitions of n.
A292454: Numbers where 4 outnumbers any other digit.
A331683: One and all numbers of the form 2^k * prime(j) for k > 0 and j already in the sequence.

Number of the day: 4507

Properties of the number 4507:

4507 is a cyclic number.
4507 is the 611^th prime.
4507 has 7 antidivisors and 4506 totatives.
Reversing the decimal digits of 4507 results in a semiprime.
4507 = 2254² - 2253² is the difference of 2 nonnegative squares in 1 way.
4507 is the sum of 2 positive triangular numbers.
4507 is the difference of 2 positive pentagonal numbers in 1 way.
4507 = 3² + 23² + 63² is the sum of 3 positive squares.
4507² is the sum of 3 positive squares.
4507 is a proper divisor of 7⁷⁵¹ - 1.
4507 is an emirp in (at least) the following bases: 2, 3, 4, 5, 11, 14, 19, 21, 22, 37, 45, 49, 50, 51, 55, 56, 57, 61, 64, 67, 69, 71, 73, 79, 83, 84, 85, 88, and 98.
4507 is palindromic in (at least) the following bases: 25, and -53.
4507 in base 24 = 7jj and consists of only the digits '7' and 'j'.
4507 in base 25 = 757 and consists of only the digits '5' and '7'.
4507 in base 33 = 44j and consists of only the digits '4' and 'j'.

The number 4507 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003375: Numbers that are the sum of 8 positive 7th powers.
A026905: Partial sums of the partition numbers A000041.
A069832: Prefixing, suffixing or inserting a 7 in the number anywhere gives a prime.
A073520: Smallest magic constant for any n X n magic square made from consecutive primes, or 0 if no such magic square exists.
A078855: Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d=2,4 or 6) and forming d-pattern=[6, 4,2]; short d-string notation of pattern = [642].
A112804: Primes such that the sum of the predecessor and successor primes is divisible by 19.
A118359: Primes for which the weight as defined in A117078 is 7 and the gap as defined in A001223 is 6.
A180803: T(n,k)=number of distinct solutions to sum{i=1..k}(x(2i-1)*x(2i)) == 0 (mod n), with x() in 0..n-1.
A215420: Primes that remain prime when a single digit 7 is inserted between any two consecutive digits or as the leading or trailing digit.
A217498: Primes of the form 2*n^2 + 58*n + 27.

Number of the day: 74957

Properties of the number 74957:

74957 is a cyclic number.
74957 = 23 × 3259 is semiprime and squarefree.
74957 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 71676 totatives.
Reversing the decimal digits of 74957 results in an emirpimes.
74957 = 37479² - 37478² = 1641² - 1618² is the difference of 2 nonnegative squares in 2 ways.
74957 is the difference of 2 positive pentagonal numbers in 2 ways.
74957 = 40² + 51² + 266² is the sum of 3 positive squares.
74957² is the sum of 3 positive squares.
74957 is a proper divisor of 853⁶⁶ - 1.
74957 = '7' + '4957' is the concatenation of 2 prime numbers.
74957 = '749' + '57' is the concatenation of 2 semiprime numbers.
74957 is an emirpimes in (at least) the following bases: 2, 4, 6, 8, 10, 12, 13, 14, 15, 17, 19, 20, 21, 22, 25, 29, 31, 33, 34, 35, 38, 39, 43, 45, 46, 49, 52, 53, 56, 57, 58, 59, 61, 64, 65, 74, 81, 83, 88, 91, 93, 95, 97, and 99.

The number 74957 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A158771: a(n) = 78*n^2 - 1.
A222151: Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..6 array extended with zeros and convolved with 1,-2,1
A229139: Smallest m such that Fibonacci(2n-1) = m^2 + k^2.

Number of the day: 5058135

Paul Cohen was born on this day 87 years ago.

Properties of the number 5058135:

5058135 = 3² × 5 × 112403 is the 4705869^th composite number and is not squarefree.
5058135 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 2697648 totatives.
5058135 = 90³ + 112³ + 143³ is the sum of 3 positive cubes in 1 way.
5058135 = 2529068² - 2529067² = 843024² - 843021² = 505816² - 505811² = 281012² - 281003² = 168612² - 168597² = 56224² - 56179² is the difference of 2 nonnegative squares in 6 ways.
5058135 is the difference of 2 positive pentagonal numbers in 2 ways.
5058135 is not the sum of 3 positive squares.
5058135² = 3034881² + 4046508² is the sum of 2 positive squares in 1 way.
5058135² is the sum of 3 positive squares.
5058135 is a proper divisor of 101⁷⁸⁴² - 1.
5058135 = '505' + '8135' is the concatenation of 2 semiprime numbers.

Number of the day: 6457

Sophie Germain was born on this day 245 years ago.

Alexander Craig Aitken was born on this day 126 years ago.

Properties of the number 6457:

6457 is a cyclic number.
6457 = 11 × 587 is semiprime and squarefree.
6457 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 5860 totatives.
6457 has a semiprime digit sum 22 in base 10.
6457 = 3229² - 3228² = 299² - 288² is the difference of 2 nonnegative squares in 2 ways.
6457 is the difference of 2 positive pentagonal numbers in 2 ways.
6457 = 7² + 18² + 78² is the sum of 3 positive squares.
6457² is the sum of 3 positive squares.
6457 is a proper divisor of 67²⁹³ - 1.
6457 is an emirpimes in (at least) the following bases: 3, 4, 5, 6, 7, 8, 9, 14, 16, 23, 24, 27, 29, 35, 37, 39, 43, 44, 51, 52, 53, 57, 58, 60, 64, 70, 75, 77, 78, 81, 85, 87, 88, 94, and 97.
6457 is palindromic in (at least) the following bases: 26, 30, and -20.
6457 in base 19 = hgg and consists of only the digits 'g' and 'h'.
6457 in base 26 = 9e9 and consists of only the digits '9' and 'e'.
6457 in base 29 = 7jj and consists of only the digits '7' and 'j'.
6457 in base 30 = 757 and consists of only the digits '5' and '7'.

The number 6457 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006457: Number of elements in Z[ i ] whose `smallest algorithm' is <= n.
A023149: Numbers k such that prime(k) == 7 (mod k).
A025235: a(n) = (1/2)*s(n+2), where s = A014431.
A068575: Numbers n such that, as strings, n is a substring of prime(n).
A243044: T(n,k)=Number of length n+3 0..k arrays with no four elements in a row with pattern abab (with a!=b) and new values 0..k introduced in 0..k order
A264099: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 363", based on the 5-celled von Neumann neighborhood.
A266778: Molien series for invariants of finite Coxeter group A_9.
A273646: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 817", based on the 5-celled von Neumann neighborhood.
A326235: Numbers n such that N = (35n)^6 is a twin rank (A002822: 6N +- 1 are twin primes).
A338453: Starts of runs of 3 consecutive numbers with the same total binary weight of their divisors (A093653).

Number of the day: 609697

René Descartes was born on this day 425 years ago.

Properties of the number 609697:

609697 is a cyclic number.
609697 = 11 × 43 × 1289 is a sphenic number and squarefree.
609697 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 540960 totatives.
609697 has an emirp digit sum 37 in base 10.
609697 = 304849² - 304848² = 27719² - 27708² = 7111² - 7068² = 881² - 408² is the difference of 2 nonnegative squares in 4 ways.
609697 is the difference of 2 positive pentagonal numbers in 3 ways.
609697 = 1² + 36² + 780² is the sum of 3 positive squares.
609697² = 264880² + 549153² is the sum of 2 positive squares in 1 way.
609697² is the sum of 3 positive squares.
609697 is a proper divisor of 419⁵⁶ - 1.
609697 in base 39 = AAXA and consists of only the digits 'A' and 'X'.

Number of the day: 9487

Stefan Banach was born on this day 129 years ago.

Properties of the number 9487:

9487 is a cyclic number.
9487 = 53 × 179 is semiprime and squarefree.
9487 has 2 distinct prime factors, 4 divisors, 25 antidivisors and 9256 totatives.
9487 has a triangular digit sum 28 in base 10.
9487 has a triangular digit product 2016 in base 10.
Reversing the decimal digits of 9487 results in an emirpimes.
9487 = 4744² - 4743² = 116² - 63² is the difference of 2 nonnegative squares in 2 ways.
9487 is the sum of 2 positive triangular numbers.
9487 is the difference of 2 positive pentagonal numbers in 1 way.
9487 is not the sum of 3 positive squares.
9487² = 5012² + 8055² is the sum of 2 positive squares in 1 way.
9487² is the sum of 3 positive squares.
9487 is a proper divisor of 1789²⁶ - 1.
9487 = '94' + '87' is the concatenation of 2 semiprime numbers.
9487 is an emirpimes in (at least) the following bases: 3, 4, 5, 6, 7, 9, 10, 11, 15, 18, 20, 21, 23, 25, 27, 31, 34, 36, 39, 42, 43, 50, 51, 55, 56, 59, 61, 65, 67, 68, 70, 71, 73, 75, 76, 79, 88, 89, 91, 95, 96, 97, 98, 99, and 100.
9487 is palindromic in (at least) base 93.
9487 in base 3 = 111000101 and consists of only the digits '0' and '1'.
9487 in base 43 = 55R and consists of only the digits '5' and 'R'.

The number 9487 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A011942: [ n(n-1)(n-2)(n-3)/32 ].
A020419: Numbers n such that continued fraction for sqrt(n) has period 80.
A022767: Ordered sequence of distinct terms of the form floor(Pi^i * floor(Pi^j)), i, j >= 0.
A031799: Period of continued fraction for sqrt(n) contains exactly 31 ones.
A035076: a(n) is root of square starting with digit 9: first term of runs.
A041540: Numerators of continued fraction convergents to sqrt(287).
A081490: Leading term of n-th row of A081491.
A194268: 8*n^2 + 7*n + 1.
A240733: Floor(6^n/(2+2*cos(Pi/9))^n).
A336561: Numbers k at which point A336459(k) appears multiplicative, but A051027(k) does not.

Number of the day: 17126756

Wilhelm Ackermann was born on this day 125 years ago.

Properties of the number 17126756:

17126756 = 2² × 31 × 59 × 2341 is the 16027811^th composite number and is not squarefree.
17126756 has 4 distinct prime factors, 24 divisors, 23 antidivisors and 8143200 totatives.
17126756 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 17126756 results in a sphenic number.
17126756 = 4281690² - 4281688² = 138150² - 138088² = 72630² - 72512² = 4170² - 512² is the difference of 2 nonnegative squares in 4 ways.
17126756 is the difference of 2 positive pentagonal numbers in 4 ways.
17126756 = 84² + 494² + 4108² is the sum of 3 positive squares.
17126756² = 10096080² + 13834556² is the sum of 2 positive squares in 1 way.
17126756² is the sum of 3 positive squares.
17126756 is a proper divisor of 709¹³⁰ - 1.

Number of the day: 13422

Alexander Grothendieck was born on this day 93 years ago.

Properties of the number 13422:

13422 = 2 × 3 × 2237 is a sphenic number and squarefree.
13422 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 4472 totatives.
13422 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 13422 results in a semiprime.
13422 is the sum of 2 positive triangular numbers.
13422 is the difference of 2 positive pentagonal numbers in 2 ways.
13422 = 1² + 14² + 115² is the sum of 3 positive squares.
13422² = 6072² + 11970² is the sum of 2 positive squares in 1 way.
13422² is the sum of 3 positive squares.
13422 is a proper divisor of 1021⁴ - 1.
13422 = '134' + '22' is the concatenation of 2 semiprime numbers.
13422 is palindromic in (at least) the following bases: 63, -25, -32, and -71.
13422 in base 62 = 3UU and consists of only the digits '3' and 'U'.

The number 13422 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A057534: a(n+1) = a(n)/2 if 2|a(n), a(n)/3 if 3|a(n), a(n)/5 if 5|a(n), a(n)/7 if 7|a(n), a(n)/11 if 11|a(n), a(n)/13 if 13|a(n), otherwise 17*a(n)+1.
A059466: Numbers which are the sum of their proper divisors containing the digit 7.
A090744: Consider numbers of the form ...53197531975319753, whose digits read from the right are 3,5,7,9,1,3,5,7,9,1,3,... Sequence gives lengths of these numbers that are primes.
A152232: Similar to A072921 but starting with 3.
A200774: Number of nX5 0..2 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
A200777: T(n,k)=Number of nXk 0..2 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
A211749: Number of -3..3 arrays x(i) of n+1 elements i=1..n+1 with set{t,u,v in 0,1}((x[i+t]+x[j+u]+x[k+v])*(-1)^(t+u+v)) having two, four, six or eight distinct values for every i,j,k<=n
A227953: Smallest m such that A070965(m) = n.
A228963: Smallest sets of 6 consecutive abundant numbers in arithmetic progression. The initial abundant number is listed.
A329665: Number of meanders of length n with Motzkin-steps avoiding the consecutive steps UD, HH and DU.

Number of the day: 922514

Properties of the number 922514:

922514 = 2 × 461257 is semiprime and squarefree.
922514 has 2 distinct prime factors, 4 divisors, 23 antidivisors and 461256 totatives.
922514 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 922514 results in an emirpimes.
922514 = 505² + 817² is the sum of 2 positive squares in 1 way.
922514 = 23² + 48² + 959² is the sum of 3 positive squares.
922514² = 412464² + 825170² is the sum of 2 positive squares in 1 way.
922514² is the sum of 3 positive squares.
922514 is a proper divisor of 107¹⁹²¹⁹ - 1.
922514 = '9' + '22514' is the concatenation of 2 semiprime numbers.
922514 is an emirpimes in (at least) the following bases: 2, 8, 10, 11, 14, 21, 25, 27, 28, 29, 30, 31, 34, 44, 56, 57, 67, 71, 80, 84, 92, 93, 96, 98, and 99.

Number of the day: 4781

Paul Erös was born on this day 108 years ago.

Properties of the number 4781:

4781 is a cyclic number.
4781 = 7 × 683 is semiprime and squarefree.
4781 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 4092 totatives.
4781 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 4781 results in an emirpimes.
4781 = 2391² - 2390² = 345² - 338² is the difference of 2 nonnegative squares in 2 ways.
4781 is the sum of 2 positive triangular numbers.
4781 is the difference of 2 positive pentagonal numbers in 2 ways.
4781 = 6² + 11² + 68² is the sum of 3 positive squares.
4781² is the sum of 3 positive squares.
4781 is a proper divisor of 1367³ - 1.
4781 = '4' + '781' is the concatenation of 2 semiprime numbers.
4781 is an emirpimes in (at least) the following bases: 3, 5, 9, 10, 11, 12, 14, 15, 16, 20, 21, 28, 29, 31, 40, 41, 43, 44, 49, 50, 53, 54, 55, 59, 63, 64, 65, 67, 70, 74, 80, 81, 83, 85, 88, 90, 91, 95, 96, and 98.
4781 is palindromic in (at least) the following bases: -2, and -59.
4781 in base 34 = 44l and consists of only the digits '4' and 'l'.

The number 4781 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000100: a(n) is the number of compositions of n in which the maximal part is 3.
A005424: Smallest number that requires n iterations of the bi-unitary totient function (A116550) to reach 1.
A025415: Least sum of 3 distinct nonzero squares in exactly n ways.
A092666: a(n) = number of Egyptian fractions 1 = 1/x_1 + ... + 1/x_k (for any k), with 0 < x_1 <= ... <= x_k = n.
A116459: Numbers n such that the minimal length of the corresponding shortest addition chain A003313(n)=A003313(3*n).
A140749: Table c(n,k) of the numerators of coefficients [x^k] P(n,x) of the polynomials P(n,x) of A129891.
A240495: Number of partitions p of n such that the multiplicity of (max(p) - min(p)) is a part.
A244803: The 360 degree spoke (or ray) of a hexagonal spiral of Ulam.
A257462: Number A(n,k) of factorizations of m^n into n factors, where m is a product of exactly k distinct primes and each factor is a product of k primes (counted with multiplicity); square array A(n,k), n>=0, k>=0, read by antidiagonals.
A300937: T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Number of the day: 424514

Properties of the number 424514:

424514 = 2 × 31 × 41 × 167 is the 388774^th composite number and is squarefree.
424514 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 199200 totatives.
424514 has an oblong digit sum 20 in base 10.
424514 = 16² + … + 108² is the sum of at least 2 consecutive positive squares in 1 way.
424514 is the difference of 2 positive pentagonal numbers in 3 ways.
424514 = 8² + 57² + 649² is the sum of 3 positive squares.
424514² = 93186² + 414160² is the sum of 2 positive squares in 1 way.
424514² is the sum of 3 positive squares.
424514 is a proper divisor of 1669¹²⁰ - 1.
424514 = '42' + '4514' is the concatenation of 2 sphenic numbers.

The number 424514 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A115080: Triangle, read by rows, where T(n,k) equals the dot product of the vector of terms in row n that are to the right of T(n,k) with the vector of terms in column k that are above T(n,k): T(n,k) = Sum_{j=0..n-k-1} T(n,j+k+1)*T(j+k,k) for n>k+1>0, with T(n,n) = 1 and T(n,n-1) = n (n>=1).
A115081: Column 0 of triangle A115080.

Number of the day: 9992109

Joseph Liouville was born on this day 212 years ago.

Properties of the number 9992109:

9992109 = 3 × 37 × 90019 is a sphenic number and squarefree.
9992109 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 6481296 totatives.
9992109 has an emirpimes digit sum 39 in base 10.
Reversing the decimal digits of 9992109 results in a sphenic number.
9992109 = 4996055² - 4996054² = 1665353² - 1665350² = 135047² - 135010² = 45065² - 44954² is the difference of 2 nonnegative squares in 4 ways.
9992109 is the sum of 2 positive triangular numbers.
9992109 is the difference of 2 positive pentagonal numbers in 2 ways.
9992109 = 208² + 227² + 3146² is the sum of 3 positive squares.
9992109² = 3240684² + 9451995² is the sum of 2 positive squares in 1 way.
9992109² is the sum of 3 positive squares.
9992109 is a proper divisor of 1231⁹ - 1.
9992109 = '9' + '992109' is the concatenation of 2 semiprime numbers.

Number of the day: 11111

Pierre-Simon Laplace was born on this day 272 years ago.

Emmy Noether was born on this day 139 years ago.

Properties of the number 11111:

11111 is a cyclic number.
11111 = 41 × 271 is semiprime and squarefree.
11111 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 10800 totatives.
11111 has a prime digit sum 5 in base 10.
11111 has a Fibonacci digit sum 5 in base 10.
11111 has a Fibonacci digit product 1 in base 10.
11111 has a triangular digit product 1 in base 10.
11111 = 5556² - 5555² = 156² - 115² is the difference of 2 nonnegative squares in 2 ways.
11111 is the difference of 2 positive pentagonal numbers in 2 ways.
11111 is not the sum of 3 positive squares.
11111² = 2439² + 10840² is the sum of 2 positive squares in 1 way.
11111² is the sum of 3 positive squares.
11111 is a proper divisor of 1439¹⁰ - 1.
11111 is an emirpimes in (at least) the following bases: 3, 5, 8, 11, 16, 17, 19, 20, 21, 22, 23, 25, 27, 29, 31, 32, 33, 35, 39, 43, 44, 49, 51, 53, 54, 55, 56, 58, 61, 65, 66, 67, 75, 77, 79, 81, 84, 85, 86, 87, 89, 96, 99, and 100.
11111 is a palindrome (in base 10).
11111 is palindromic in (at least) base 69.
11111 consists of only the digit '1'.

The number 11111 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000042: Unary representation of natural numbers.
A002275: Repunits: (10^n - 1)/9. Often denoted by R_n.
A002778: Numbers whose square is a palindrome.
A004676: Primes written in base 2.
A007088: The binary numbers (or binary words, or binary vectors): numbers written in base 2.
A007931: Numbers that contain only 1's and 2's. Nonempty binary strings of length n in lexicographic order.
A010785: Repdigit numbers, or numbers with repeated digits.
A039724: Numbers in base -2.
A053699: a(n) = n^4 + n^3 + n^2 + n + 1.
A057148: Palindromes only using 0 and 1 (i.e., base 2 palindromes).

Number of the day: 51371

Properties of the number 51371:

51371 is a cyclic number.
51371 = 47 × 1093 is semiprime and squarefree.
51371 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 50232 totatives.
51371 has an emirp digit sum 17 in base 10.
51371 has a sphenic digit product 105 in base 10.
51371 has a triangular digit product 105 in base 10.
Reversing the decimal digits of 51371 results in an emirpimes.
51371 = 25686² - 25685² = 570² - 523² is the difference of 2 nonnegative squares in 2 ways.
51371 is the difference of 2 positive pentagonal numbers in 2 ways.
51371 = 11² + 25² + 225² is the sum of 3 positive squares.
51371² = 6204² + 50995² is the sum of 2 positive squares in 1 way.
51371² is the sum of 3 positive squares.
51371 is a proper divisor of 941³ - 1.
51371 = '51' + '371' is the concatenation of 2 semiprime numbers.
51371 is an emirpimes in (at least) the following bases: 4, 5, 6, 7, 10, 11, 14, 23, 24, 27, 33, 34, 36, 37, 38, 39, 43, 44, 49, 52, 58, 59, 60, 62, 66, 67, 81, 82, 83, 84, 85, 88, 89, 92, and 94.
51371 is palindromic in (at least) the following bases: 54, -45, and -50.
51371 in base 42 = T55 and consists of only the digits '5' and 'T'.
51371 in base 44 = QNN and consists of only the digits 'N' and 'Q'.
51371 in base 49 = LJJ and consists of only the digits 'J' and 'L'.
51371 in base 54 = HXH and consists of only the digits 'H' and 'X'.
51371 in base 58 = FFf and consists of only the digits 'F' and 'f'.

The number 51371 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A008384: Crystal ball sequence for A_4 lattice.
A234729: Volume of right regular hexagonal pyramid with height and side lengths n, rounded down.

Number of the day: 70881

Joseph Fourier was born on this day 253 years ago.

George David Birkhoff was born on this day 137 years ago.

Properties of the number 70881:

70881 is a cyclic number.
70881 = 3 × 23627 is semiprime and squarefree.
70881 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 47252 totatives.
Reversing the decimal digits of 70881 results in an emirpimes.
70881 = 35441² - 35440² = 11815² - 11812² is the difference of 2 nonnegative squares in 2 ways.
70881 is the difference of 2 positive pentagonal numbers in 1 way.
70881 = 11² + 46² + 262² is the sum of 3 positive squares.
70881² is the sum of 3 positive squares.
70881 is a proper divisor of 19¹¹⁸¹³ - 1.
70881 is an emirpimes in (at least) the following bases: 3, 6, 9, 10, 19, 21, 28, 31, 34, 35, 36, 42, 43, 45, 49, 53, 55, 63, 69, 71, 72, 75, 80, 83, 88, 90, and 100.
70881 in base 55 = NNf and consists of only the digits 'N' and 'f'.

Number of the day: 77737

Alfréd Rényi was born on this day 100 years ago.

Properties of the number 77737:

77737 is a cyclic number.
77737 = 11 × 37 × 191 is a sphenic number and squarefree.
77737 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 68400 totatives.
77737 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 77737 results in a sphenic number.
77737 = 38869² - 38868² = 3539² - 3528² = 1069² - 1032² = 299² - 108² is the difference of 2 nonnegative squares in 4 ways.
77737 is the sum of 2 positive triangular numbers.
77737 is the difference of 2 positive pentagonal numbers in 3 ways.
77737 = 42² + 97² + 258² is the sum of 3 positive squares.
77737² = 25212² + 73535² is the sum of 2 positive squares in 1 way.
77737² is the sum of 3 positive squares.
77737 is a proper divisor of 1153²⁰ - 1.
77737 = '77' + '737' is the concatenation of 2 semiprime numbers.
77737 is palindromic in (at least) base 67.
77737 consists of only the digits '3' and '7'.

The number 77737 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A043520: Numbers such that the number of 7's in their decimal representation is 4.

Number of the day: 6892

Properties of the number 6892:

6892 = 2² × 1723 is the 6005^th composite number and is not squarefree.
6892 has 2 distinct prime factors, 6 divisors, 13 antidivisors and 3444 totatives.
6892 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 6892 results in a semiprime.
6892 = 1724² - 1722² is the difference of 2 nonnegative squares in 1 way.
6892 is the difference of 2 positive pentagonal numbers in 1 way.
6892 = 18² + 22² + 78² is the sum of 3 positive squares.
6892² is the sum of 3 positive squares.
6892 is a proper divisor of 41³ - 1.
6892 is palindromic in (at least) the following bases: 41, 53, -42, and -65.
6892 in base 40 = 4CC and consists of only the digits '4' and 'C'.
6892 in base 41 = 444 and consists of only the digit '4'.
6892 in base 52 = 2SS and consists of only the digits '2' and 'S'.
6892 in base 53 = 2O2 and consists of only the digits '2' and 'O'.
6892 in base 58 = 22m and consists of only the digits '2' and 'm'.

The number 6892 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A020169: Pseudoprimes to base 41.
A079104: Number of permutations of length n containing the minimum number of monotone subsequences of length 4.
A079105: Number of permutations of length n, in which all monotone subsequences of length 4 are descending or all such subsequences are ascending, containing the minimum number of such subsequences subject to that constraint.
A103198: Number of compositions of n into a square number of parts.
A112087: 4*(n^2 - n + 1).
A130442: Even pseudoprimes to base 41.
A192531: Monotonic ordering of set S generated by these rules:if x and y are in S then 3xy-2x-2y is in S, and 2 is in S.
A212579: Number of (w,x,y,z) with all terms in {1,...,n} and min{|w-x|,|w-y|}=min{|x-y|,|x-z|}.
A263149: Expansion of Product_{k>=1} (1 + x^(2*k+1))^k.
A280611: Number of degree n products of distinct cyclotomic polynomials.

Number of the day: 668

Christian Goldbach was born on this day 331 years ago.

Properties of the number 668:

668 = 2² × 167 is the 546^th composite number and is not squarefree.
668 has 2 distinct prime factors, 6 divisors, 9 antidivisors and 332 totatives.
668 has an oblong digit sum 20 in base 10.
668 has sum of divisors equal to 1176 which is a triangular number.
Reversing the decimal digits of 668 results in a semiprime.
668 = 168² - 166² is the difference of 2 nonnegative squares in 1 way.
668 is the difference of 2 positive pentagonal numbers in 1 way.
668 is not the sum of 3 positive squares.
668² is the sum of 3 positive squares.
668 is a proper divisor of 1669² - 1.
668 is palindromic in (at least) the following bases: 18, 23, and -29.
668 in base 3 = 220202 and consists of only the digits '0' and '2'.
668 in base 9 = 822 and consists of only the digits '2' and '8'.
668 consists of only the digits '6' and '8'.
668 in base 11 = 558 and consists of only the digits '5' and '8'.
668 in base 17 = 255 and consists of only the digits '2' and '5'.
668 in base 18 = 212 and consists of only the digits '1' and '2'.
668 in base 22 = 188 and consists of only the digits '1' and '8'.
668 in base 23 = 161 and consists of only the digits '1' and '6'.
668 in base 25 = 11i and consists of only the digits '1' and 'i'.

The number 668 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000009: Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts.
A005823: Numbers whose ternary expansion contains no 1's.
A026769: Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; T(2,1)=2; for n >= 3 and 1<=k<=n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if 1<=k<=(n-1)/2, else T(n,k) = T(n-1,k-1) + T(n-1,k).
A051225: Numbers m such that the Bernoulli number B_{2*m} has denominator 30.
A051226: Numbers m such that the Bernoulli number B_m has denominator 30.
A080054: G.f.: Product_{n >= 0} (1+x^(2n+1))/(1-x^(2n+1)).
A143823: Number of subsets {x(1),x(2),...,x(k)} of {1,2,...,n} such that all differences |x(i)-x(j)| are distinct.
A161330: Snowflake (or E-toothpick) sequence (see Comments lines for definition).
A161424: Numbers k whose largest divisor <= sqrt(k) equals 4.
A235229: Numbers whose sum of digits is 20.

Number of the day: 793290

Properties of the number 793290:

793290 = 2 × 3 × 5 × 31 × 853 is the 729837^th composite number and is squarefree.
793290 has 5 distinct prime factors, 32 divisors, 17 antidivisors and 204480 totatives.
793290 has a sphenic digit sum 30 in base 10.
793290 has an oblong digit sum 30 in base 10.
793290 is the sum of 2 positive triangular numbers.
793290 is the difference of 2 positive pentagonal numbers in 4 ways.
793290 = 37² + 40² + 889² is the sum of 3 positive squares.
793290² = 475974² + 634632² = 309504² + 730422² = 501642² + 614544² = 190650² + 770040² is the sum of 2 positive squares in 4 ways.
793290² is the sum of 3 positive squares.
793290 is a proper divisor of 1373⁶⁰ - 1.

Number of the day: 90563

Properties of the number 90563:

90563 is a cyclic number.
90563 = 11 × 8233 is semiprime and squarefree.
90563 has 2 distinct prime factors, 4 divisors, 51 antidivisors and 82320 totatives.
90563 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 90563 results in an emirpimes.
90563 = 45282² - 45281² = 4122² - 4111² is the difference of 2 nonnegative squares in 2 ways.
90563 is the difference of 2 positive pentagonal numbers in 2 ways.
90563 = 15² + 67² + 293² is the sum of 3 positive squares.
90563² = 39875² + 81312² is the sum of 2 positive squares in 1 way.
90563² is the sum of 3 positive squares.
90563 is a proper divisor of 353⁵⁶ - 1.
90563 is an emirpimes in (at least) the following bases: 4, 7, 8, 9, 10, 11, 15, 16, 20, 23, 26, 29, 30, 33, 36, 38, 46, 51, 53, 55, 59, 60, 63, 64, 68, 71, 73, 76, 79, 89, 91, 95, and 96.
90563 is palindromic in (at least) the following bases: 88, and -47.

The number 90563 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A229257: O.g.f.: Sum_{n>=0} x^n / Product_{k=1..n} (1 - n^2*k*x).

Number of the day: 661057

Properties of the number 661057:

661057 is a cyclic number.
661057 = 61 × 10837 is semiprime and squarefree.
661057 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 650160 totatives.
661057 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 661057 results in an emirpimes.
661057 = 330529² - 330528² = 5449² - 5388² is the difference of 2 nonnegative squares in 2 ways.
661057 is the difference of 2 positive pentagonal numbers in 2 ways.
661057 = 264² + 769² = 121² + 804² is the sum of 2 positive squares in 2 ways.
661057 = 14² + 69² + 810² is the sum of 3 positive squares.
661057² = 194568² + 631775² = 119207² + 650220² = 406032² + 521665² = 305305² + 586332² is the sum of 2 positive squares in 4 ways.
661057² is the sum of 3 positive squares.
661057 is a proper divisor of 367²⁵² - 1.
661057 is an emirpimes in (at least) the following bases: 7, 10, 11, 12, 17, 19, 25, 26, 28, 29, 31, 33, 37, 44, 45, 48, 50, 53, 55, 59, 64, 67, 69, 70, 74, 76, 78, 79, 80, 83, 85, 88, 91, 92, 93, 95, and 100.
661057 is palindromic in (at least) base -18.
661057 in base 60 = 33bb and consists of only the digits '3' and 'b'.

Number of the day: 480424

Properties of the number 480424:

480424 = 2³ × 7 × 23 × 373 is the 440383^th composite number and is not squarefree.
480424 has 4 distinct prime factors, 32 divisors, 23 antidivisors and 196416 totatives.
480424 has a semiprime digit sum 22 in base 10.
480424 = 120107² - 120105² = 60055² - 60051² = 17165² - 17151² = 8593² - 8565² = 5245² - 5199² = 2657² - 2565² = 907² - 585² = 695² - 51² is the difference of 2 nonnegative squares in 8 ways.
480424 is the sum of 2 positive triangular numbers.
480424 is the difference of 2 positive pentagonal numbers in 5 ways.
480424 = 72² + 218² + 654² is the sum of 3 positive squares.
480424² = 324576² + 354200² is the sum of 2 positive squares in 1 way.
480424² is the sum of 3 positive squares.
480424 is a proper divisor of 461⁶ - 1.
480424 in base 7 = 4040440 and consists of only the digits '0' and '4'.
480424 in base 49 = 444S and consists of only the digits '4' and 'S'.

Number of the day: 8659

Properties of the number 8659:

8659 is a cyclic number.
8659 = 7 × 1237 is semiprime and squarefree.
8659 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 7416 totatives.
8659 has a triangular digit sum 28 in base 10.
8659 = 4330² - 4329² = 622² - 615² is the difference of 2 nonnegative squares in 2 ways.
8659 is the difference of 2 positive pentagonal numbers in 2 ways.
8659 = 1² + 3² + 93² is the sum of 3 positive squares.
8659² = 4284² + 7525² is the sum of 2 positive squares in 1 way.
8659² is the sum of 3 positive squares.
8659 is a proper divisor of 937⁶ - 1.
8659 = '865' + '9' is the concatenation of 2 semiprime numbers.
8659 is an emirpimes in (at least) the following bases: 7, 13, 14, 16, 18, 21, 23, 26, 27, 34, 37, 47, 53, 59, 65, 68, 69, 70, 71, 72, 75, 77, 79, 80, 82, 83, 86, 87, 89, 90, 91, 92, 94, 97, and 98.
8659 is palindromic in (at least) the following bases: 3, 74, and 78.
8659 in base 46 = 44B and consists of only the digits '4' and 'B'.

The number 8659 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A038156: a(n) = n! * Sum_{k=1..n-1} 1/k!.
A060879: Intrinsic 9-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.
A069126: Centered 13-gonal numbers.
A082459: Multiply by 1, add 1, multiply by 2, add 2, etc.
A121662: Triangle read by rows: T(i,j) for the recurrence T(i,j)=(T(i-1)+1,j)*i.
A127524: Number of unordered rooted trees where each subtree from given node has the same number of nodes.
A174286: Number of distinct resistances that can be produced using at most n equal resistors in series and/or parallel, confined to the five arms (four arms and the diagonal) of a bridge configuration. Since the bridge requires a minimum of five resistors, the first four terms are zero.
A205768: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having nonzero determinant and having the same number of clockwise edge increases as its horizontal and vertical neighbors
A247294: Triangle read by rows: T(n,k) is the number of weighted lattice paths B(n) having a total of k uhd and uHd strings.
A247295: Number of weighted lattice paths B(n) having no uhd and no uHd strings.

Number of the day: 61091

Properties of the number 61091:

61091 is a cyclic number.
61091 is the 6153^th prime.
61091 has 9 antidivisors and 61090 totatives.
61091 has an emirp digit sum 17 in base 10.
61091 = 30546² - 30545² is the difference of 2 nonnegative squares in 1 way.
61091 is the difference of 2 positive pentagonal numbers in 1 way.
61091 = 1² + 9² + 247² is the sum of 3 positive squares.
61091² is the sum of 3 positive squares.
61091 is a proper divisor of 1087¹⁴⁹ - 1.
61091 is an emirp in (at least) the following bases: 2, 4, 6, 11, 14, 19, 31, 44, 49, 53, 56, 61, 65, 68, 72, 74, 77, 79, 82, 89, 90, and 92.
61091 is palindromic in (at least) base 95.

The number 61091 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A153402: Smaller of 3 consecutive prime numbers such that p1*p2*p3+d1+d2-1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.
A337251: Positive integers k such that k^2 = A^2+B^2+C^2 and A^3+B^3+C^3 = m^3, where gcd(A,B,C) = 1 and A, B, C, m are positive integers.

Number of the day: 334

Properties of the number 334:

334 = 2 × 167 is semiprime and squarefree.
334 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 166 totatives.
334 has a semiprime digit sum 10 in base 10.
334 has a triangular digit sum 10 in base 10.
334 has a triangular digit product 36 in base 10.
Reversing the decimal digits of 334 results in a prime.
334 is the difference of 2 positive pentagonal numbers in 2 ways.
334 = 3² + 10² + 15² is the sum of 3 positive squares.
334² is the sum of 3 positive squares.
334 is a proper divisor of 1669² - 1.
334 = '33' + '4' is the concatenation of 2 semiprime numbers.
334 = '3' + '34' is the concatenation of 2 Fibonacci numbers.
334 is an emirpimes in (at least) the following bases: 3, 5, 9, 12, 13, 14, 15, 16, 17, 18, 19, 29, 32, 33, 34, 35, 37, 39, 41, 42, 45, 46, 49, 50, 55, 56, 57, 59, 60, 61, 63, 64, 67, 69, 71, 75, 84, 85, 86, 91, 92, 94, 97, and 100.
334 is palindromic in (at least) the following bases: -8, -10, and -37.
334 in base 3 = 110101 and consists of only the digits '0' and '1'.
334 in base 7 = 655 and consists of only the digits '5' and '6'.
334 in base 9 = 411 and consists of only the digits '1' and '4'.
334 consists of only the digits '3' and '4'.

The number 334 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000068: Numbers n such that n^4 + 1 is prime.
A003052: Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m).
A003278: Szekeres's sequence: a(n)-1 in ternary = n-1 in binary; also: a(1) = 1, a(2) = 2, and thereafter a(n) is smallest number k which avoids any 3-term arithmetic progression in a(1), a(2), ..., a(n-1), k.
A005237: Numbers n such that n and n+1 have the same number of divisors.
A005836: Numbers n whose base 3 representation contains no 2.
A100484: Even semiprimes.
A108917: Number of knapsack partitions of n.
A161344: Numbers k with A033676(k)=2, where A033676 is the largest divisor <= sqrt(k).
A191113: Increasing sequence generated by these rules:a(1)=1, and if x is in a then 3x-2 and 4x-2 are in a.
A210000: Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n}.

Number of the day: 456564

Properties of the number 456564:

456564 = 2² × 3 × 38047 is the 418358^th composite number and is not squarefree.
456564 has 3 distinct prime factors, 12 divisors, 7 antidivisors and 152184 totatives.
456564 has a sphenic digit sum 30 in base 10.
456564 has an oblong digit sum 30 in base 10.
456564 = 114142² - 114140² = 38050² - 38044² is the difference of 2 nonnegative squares in 2 ways.
456564 is the sum of 2 positive triangular numbers.
456564 is the difference of 2 positive pentagonal numbers in 1 way.
456564 = 28² + 122² + 664² is the sum of 3 positive squares.
456564² is the sum of 3 positive squares.
456564 is a proper divisor of 1231³⁴ - 1.