Number of the day: 1667613

Carl Ludwig Siegel was born on this day 120 years ago.

Properties of the number 1667613:

1667613 = 3 × 555871 is semiprime and squarefree.
1667613 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 1111740 totatives.
1667613 has a sphenic digit sum 30 in base 10.
1667613 has an oblong digit sum 30 in base 10.
1667613 = 833807² - 833806² = 277937² - 277934² is the difference of 2 nonnegative squares in 2 ways.
1667613 is the difference of 2 positive pentagonal numbers in 1 way.
1667613 = 38² + 85² + 1288² is the sum of 3 positive squares.
1667613² is the sum of 3 positive squares.
1667613 is a divisor of 1237²⁶⁴⁷ - 1.
1667613 = '1667' + '613' is the concatenation of 2 prime numbers.
1667613 = '166' + '7613' is the concatenation of 2 semiprime numbers.
1667613 is an emirpimes in (at least) the following bases: 11, 15, 21, 25, 26, 27, 33, 34, 35, 36, 53, 56, 69, 73, 76, 81, 84, 87, 91, 93, 96, 98, and 99.

Number of the day: 83726

Properties of the number 83726:

83726 = 2 × 41863 is semiprime and squarefree.
83726 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 41862 totatives.
83726 has an emirpimes digit sum 26 in base 10.
83726 has a triangular digit product 2016 in base 10.
83726 = 39² + 46² + 283² is the sum of 3 positive squares.
83726² is the sum of 3 positive squares.
83726 is a divisor of 7⁶⁹⁷⁷ - 1.
83726 = '8372' + '6' is the concatenation of 2 oblong numbers.
83726 is an emirpimes in (at least) the following bases: 2, 8, 16, 19, 22, 23, 26, 29, 36, 39, 40, 45, 47, 50, 51, 53, 56, 57, 59, 62, 65, 69, 71, 74, 78, 83, 85, 86, 87, 91, 94, and 99.
83726 is palindromic in (at least) the following bases: 49, 68, and -71.
83726 in base 23 = 6k66 and consists of only the digits '6' and 'k'.
83726 in base 49 = YgY and consists of only the digits 'Y' and 'g'.

The number 83726 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A239687: Numbers n such that if n = a U b (where U denotes concatenation) then abs(sigma*(a) - sigma*(b)) = abs(sigma*(n) - n), where sigma*(n) is the sum of the anti-divisors of n.

Number of the day: 6045351383

Properties of the number 6045351383:

6045351383 = 2539 × 2380997 is semiprime and squarefree.
6045351383 has 2 distinct prime factors, 4 divisors, 47 antidivisors and 6042967848 totatives.
6045351383 has a semiprime digit sum 38 in base 10.
Reversing the decimal digits of 6045351383 results in a sphenic number.
6045351383 = 3022675692² - 3022675691² = 1191768² - 1189229² is the difference of 2 nonnegative squares in 2 ways.
6045351383 is the sum of 2 positive triangular numbers.
6045351383 is the difference of 2 positive pentagonal numbers in 2 ways.
6045351383 is not the sum of 3 positive squares.
6045351383² = 3480897908² + 4942633215² is the sum of 2 positive squares in 1 way.
6045351383² is the sum of 3 positive squares.
6045351383 is a divisor of 307^3571494 - 1.
6045351383 = '604535' + '1383' is the concatenation of 2 semiprime numbers.
6045351383 is an emirpimes in (at least) the following bases: 8, 13, 16, 19, 24, 26, 27, 31, 36, 37, 39, 41, 42, 45, 51, 52, 53, 73, 77, 80, 81, 84, 88, 97, and 98.

Number of the day: 9125223

John von Neumann was born on this day 113 years ago.

Properties of the number 9125223:

9125223 = 3 × 3041741 is semiprime and squarefree.
9125223 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 6083480 totatives.
Reversing the decimal digits of 9125223 results in an emirpimes.
9125223 = 4562612² - 4562611² = 1520872² - 1520869² is the difference of 2 nonnegative squares in 2 ways.
9125223 is the difference of 2 positive pentagonal numbers in 1 way.
9125223 is not the sum of 3 positive squares.
9125223² = 2293980² + 8832177² is the sum of 2 positive squares in 1 way.
9125223² is the sum of 3 positive squares.
9125223 is a divisor of 173²³³⁹⁸ - 1.
9125223 = '91' + '25223' is the concatenation of 2 semiprime numbers.
9125223 is an emirpimes in (at least) the following bases: 9, 10, 14, 31, 39, 40, 41, 49, 51, 52, 56, 57, 61, 71, 78, 83, 87, and 92.

Number of the day: 5368647660488

Johannes Kepler was born on this day 445 years ago.

Johannes Kepler was born on this day 445 years ago.

Jacob Bernoulli was born on this day 362 years ago.

Properties of the number 5368647660488:

5368647660488 = 2³ × 7 × 337 × 3301 × 86179 is composite and not squarefree.
5368647660488 has 5 distinct prime factors, 64 divisors, 67 antidivisors and 2293299993600 totatives.
5368647660488 has an emirp digit sum 71 in base 10.
5368647660488 is the difference of 2 nonnegative squares in 16 ways.
5368647660488 = 402² + 7520² + 2317022² is the sum of 3 positive squares.
5368647660488² = 2787873414200² + 4588043104512² = 396757085088² + 5353966895480² = 2818615187080² + 4569221610912² = 2441181502088² + 4781528058720² is the sum of 2 positive squares in 4 ways.
5368647660488² is the sum of 3 positive squares.
5368647660488 is a divisor of 1889⁶⁹⁹⁶⁰⁰ - 1.

Number of the day: 568861

Charles Babbage was born on this day 225 years ago.

Properties of the number 568861:

568861 = 619 × 919 is semiprime and squarefree.
568861 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 567324 totatives.
568861 has a semiprime digit sum 34 in base 10.
568861 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 568861 results in an emirpimes.
568861 = 284431² - 284430² = 769² - 150² is the difference of 2 nonnegative squares in 2 ways.
568861 is the difference of 2 positive pentagonal numbers in 1 way.
568861 = 40² + 69² + 750² is the sum of 3 positive squares.
568861² is the sum of 3 positive squares.
568861 is a divisor of 367⁵⁴ - 1.
568861 is an emirpimes in (at least) the following bases: 2, 3, 6, 8, 10, 13, 18, 20, 24, 25, 27, 28, 41, 44, 47, 49, 55, 56, 61, 64, 65, 66, 72, 73, 76, 80, 81, 82, 83, 85, 88, 92, 93, and 94.
568861 is palindromic in (at least) base 96.

Number of the day: 219320

Properties of the number 219320:

219320 = 2³ × 5 × 5483 is the 199766^th composite number and is not squarefree.
219320 has 3 distinct prime factors, 16 divisors, 11 antidivisors and 87712 totatives.
219320 has an emirp digit sum 17 in base 10.
219320 = 54831² - 54829² = 27417² - 27413² = 10971² - 10961² = 5493² - 5473² is the difference of 2 nonnegative squares in 4 ways.
219320 is the difference of 2 positive pentagonal numbers in 2 ways.
219320 = 20² + 42² + 466² is the sum of 3 positive squares.
219320² = 131592² + 175456² is the sum of 2 positive squares in 1 way.
219320² is the sum of 3 positive squares.
219320 is a divisor of 241²⁷⁴¹ - 1.
219320 is palindromic in (at least) base -93.

Number of the day: 4487657896

Charles Hermite was born on this day 194 years ago.

Properties of the number 4487657896:

4487657896 = 2³ × 29 × 107 × 180779 is the 4275699477^th composite number and is not squarefree.
4487657896 has 4 distinct prime factors, 32 divisors, 35 antidivisors and 2146196416 totatives.
4487657896 = 1121914475² - 1121914473² = 560957239² - 560957235² = 38686735² - 38686677² = 19343411² - 19343295² = 10485289² - 10485075² = 5242805² - 5242377² = 364661² - 358455² = 186985² - 174573² is the difference of 2 nonnegative squares in 8 ways.
4487657896 is the sum of 2 positive triangular numbers.
4487657896 is the difference of 2 positive pentagonal numbers in 4 ways.
4487657896 = 2406² + 2944² + 66882² is the sum of 3 positive squares.
4487657896² = 3094936480² + 3249683304² is the sum of 2 positive squares in 1 way.
4487657896² is the sum of 3 positive squares.
4487657896 is a divisor of 523⁴³³⁵⁴ - 1.

Number of the day: 2945

Properties of the number 2945:

2945 = 5 × 19 × 31 is a sphenic number and squarefree.
2945 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 2160 totatives.
2945 has an oblong digit sum 20 in base 10.
2945 = 1473² - 1472² = 297² - 292² = 87² - 68² = 63² - 32² is the difference of 2 nonnegative squares in 4 ways.
2945 is the difference of 2 positive pentagonal numbers in 3 ways.
2945 = 2² + 5² + 54² is the sum of 3 positive squares.
2945² = 1767² + 2356² is the sum of 2 positive squares in 1 way.
2945² is the sum of 3 positive squares.
2945 is a divisor of 1861² - 1.
2945 is palindromic in (at least) the following bases: 46, 94, -64, and -92.
2945 in base 20 = 775 and consists of only the digits '5' and '7'.
2945 in base 45 = 1KK and consists of only the digits '1' and 'K'.
2945 in base 46 = 1I1 and consists of only the digits '1' and 'I'.

The number 2945 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A011257: Geometric mean of phi(n) and sigma(n) is an integer.
A026797: Number of partitions of n in which the least part is 4.
A038691: Prime race 4k-1 vs. 4k+1 is tied at n-th prime.
A045944: Rhombic matchstick numbers: n*(3*n+2).
A050059: a(n)=a(n-1)+a(m), where m=2n-2-2^(p+1) and 2^p<n-1<=2^(p+1), for n >= 4.
A081377: Numbers n such that the set of prime divisors of phi(n) is equal to the set of prime divisors of sigma(n).
A089558: a(n)=A089551(n)/2.
A139593: A139276(n) followed by A139272(n+1).
A219038: Numbers n such that 3^n - 14 is prime.
A246326: Total number of ON cells at stage n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 454".

Number of the day: 946755

Srinivasa Ramanujan was born on this day 129 years ago.

Properties of the number 946755:

946755 = 3³ × 5 × 7013 is the 872075^th composite number and is not squarefree.
946755 has 3 distinct prime factors, 16 divisors, 23 antidivisors and 504864 totatives.
946755 has a triangular digit sum 36 in base 10.
946755 = 473378² - 473377² = 157794² - 157791² = 94678² - 94673² = 52602² - 52593² = 31566² - 31551² = 17546² - 17519² = 10542² - 10497² = 3574² - 3439² is the difference of 2 nonnegative squares in 8 ways.
946755 is the difference of 2 positive pentagonal numbers in 2 ways.
946755 = 1² + 5² + 973² is the sum of 3 positive squares.
946755² = 568053² + 757404² = 469152² + 822339² = 220131² + 920808² = 376380² + 868725² is the sum of 2 positive squares in 4 ways.
946755² is the sum of 3 positive squares.
946755 is a divisor of 271¹⁷⁵³ - 1.

Number of the day: 5347

Properties of the number 5347:

5347 is the 707^th prime.
5347 has 19 antidivisors and 5346 totatives.
5347 has a prime digit sum 19 in base 10.
5347 has an oblong digit product 420 in base 10.
Reversing the decimal digits of 5347 results in a semiprime.
5347 = 2674² - 2673² is the difference of 2 nonnegative squares in 1 way.
5347 is the sum of 2 positive triangular numbers.
5347 is the difference of 2 positive pentagonal numbers in 1 way.
5347 = 15² + 19² + 69² is the sum of 3 positive squares.
5347² is the sum of 3 positive squares.
5347 is a divisor of 479³ - 1.
5347 = '5' + '347' is the concatenation of 2 prime numbers.
5347 is an emirp in (at least) the following bases: 2, 16, 19, 20, 25, 26, 29, 31, 32, 33, 38, 41, 49, 52, 55, 56, 57, 58, 61, 62, 63, 64, 65, 70, 71, 72, 73, 75, 77, 82, 83, 85, 87, 89, 90, 91, and 95.
5347 is palindromic in (at least) the following bases: 54, 66, -21, -23, -39, -81, and -99.
5347 in base 20 = d77 and consists of only the digits '7' and 'd'.
5347 in base 22 = b11 and consists of only the digits '1' and 'b'.
5347 in base 36 = 44j and consists of only the digits '4' and 'j'.
5347 in base 51 = 22h and consists of only the digits '2' and 'h'.
5347 in base 53 = 1ll and consists of only the digits '1' and 'l'.
5347 in base 54 = 1j1 and consists of only the digits '1' and 'j'.

The number 5347 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A053253: Coefficients of the '3rd order' mock theta function omega(q)
A082077: Balanced primes of order two.
A088784: Primes formed by concatenating a prime with the preceding prime.
A096698: Balanced primes of order six.
A096706: Balanced primes (A090403) of index 2.
A108054: Integers n such that 10^n+49 is prime.
A120214: Start with 1013 and repeatedly reverse the digits and add 2 to get the next term.
A136064: Mother primes of order 5.
A255206: Primes p for which exactly three bases b with 1 < b < p exist such that p is a base b Wieferich prime.
A260553: Primes p such that p = q^2 + 2*r^2 where q and r are also primes.

Number of the day: 3026

Properties of the number 3026:

3026 = 2 × 17 × 89 is a sphenic number and squarefree.
3026 has 3 distinct prime factors, 8 divisors, 5 antidivisors and 1408 totatives.
3026 has a prime digit sum 11 in base 10.
Reversing the decimal digits of 3026 results in a prime.
3026 = 10² + … + 21² is the sum of at least 2 consecutive positive squares in 1 way.
3026 is the sum of 2 positive triangular numbers.
3026 is the difference of 2 positive pentagonal numbers in 1 way.
3026 = 25² + 49² = 1² + 55² is the sum of 2 positive squares in 2 ways.
3026 = 19² + 36² + 37² is the sum of 3 positive squares.
3026² = 1424² + 2670² = 110² + 3024² = 1776² + 2450² = 1326² + 2720² is the sum of 2 positive squares in 4 ways.
3026² is the sum of 3 positive squares.
3026 is a divisor of 1123⁴ - 1.
3026 = '302' + '6' is the concatenation of 2 semiprime numbers.
3026 is palindromic in (at least) the following bases: 36, 55, 88, -42, -48, -54, and -55.
3026 in base 6 = 22002 and consists of only the digits '0' and '2'.
3026 in base 27 = 442 and consists of only the digits '2' and '4'.
3026 in base 35 = 2gg and consists of only the digits '2' and 'g'.
3026 in base 36 = 2c2 and consists of only the digits '2' and 'c'.
3026 in base 54 = 122 and consists of only the digits '1' and '2'.
3026 in base 55 = 101 and consists of only the digits '0' and '1'.

The number 3026 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003336: Numbers that are the sum of 2 nonzero 4th powers.
A035959: Number of partitions of n in which no parts are multiples of 5.
A059929: a(n) = Fibonacci(n)*Fibonacci(n+2).
A069894: Centered square numbers: 4*n^2 + 4*n + 2.
A070550: a(n) = a(n-1) + a(n-3) + a(n-4), starting with a(0..3) = 1, 2, 2, 3.
A075205: Number of polyominoes with n cells that tile the plane isohedrally.
A092229: Numbers n such that numerator of Bernoulli(2n) is divisible by 257, the tenth irregular prime.
A133535: Sum of fourth powers of two consecutive primes.
A134406: Composite numbers of the form n^2 + 1.
A264272: T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having index change +-(.,.) 0,0 1,0 or 1,2.

Number of the day: 19525655079

Properties of the number 19525655079:

19525655079 = 3² × 7 × 29 × 10687277 is composite and not squarefree.
19525655079 has 4 distinct prime factors, 24 divisors, 31 antidivisors and 10772774208 totatives.
19525655079 is the difference of 2 nonnegative squares in 12 ways.
19525655079 is the difference of 2 positive pentagonal numbers in 4 ways.
19525655079 is not the sum of 3 positive squares.
19525655079² = 13465969020² + 14139267471² = 6590819655² + 18379670904² = 5686946496² + 18679128615² = 8764023996² + 17448297615² is the sum of 2 positive squares in 4 ways.
19525655079² is the sum of 3 positive squares.
19525655079 is a divisor of 307^10687276 - 1.
19525655079 = '195' + '25655079' is the concatenation of 2 sphenic numbers.

Number of the day: 6667

Properties of the number 6667:

6667 = 59 × 113 is semiprime and squarefree.
6667 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 6496 totatives.
6667 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 6667 results in an emirpimes.
6667 = 3334² - 3333² = 86² - 27² is the difference of 2 nonnegative squares in 2 ways.
6667 is the sum of 2 positive triangular numbers.
6667 is the difference of 2 positive pentagonal numbers in 1 way.
6667 = 5² + 9² + 81² is the sum of 3 positive squares.
6667² = 885² + 6608² is the sum of 2 positive squares in 1 way.
6667² is the sum of 3 positive squares.
6667 is a divisor of 1061⁸ - 1.
6667 = '6' + '667' is the concatenation of 2 semiprime numbers.
6667 is an emirpimes in (at least) the following bases: 4, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 21, 22, 24, 25, 31, 33, 35, 38, 43, 44, 46, 51, 52, 57, 58, 60, 61, 64, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 83, 85, 88, 91, 93, 95, 96, and 98.
6667 is palindromic in (at least) the following bases: 2, 30, 66, -6, -49, and -56.
6667 consists of only the digits '6' and '7'.
6667 in base 29 = 7qq and consists of only the digits '7' and 'q'.
6667 in base 30 = 7c7 and consists of only the digits '7' and 'c'.
6667 in base 36 = 557 and consists of only the digits '5' and '7'.
6667 in base 57 = 22t and consists of only the digits '2' and 't'.

The number 6667 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A035349: "DIK" (bracelet, indistinct, unlabeled) transform of A000237.
A051003: Beastly (or hateful) numbers: numbers containing the string 666 in their decimal expansion.
A067275: Number of Fibonacci numbers A000045(k), k <= 10^n, which end in 4.
A080859: a(n) = 6*n^2 + 4*n + 1.
A088797: Numbers n>2 such that n divides the concatenation of n-2 and n-1.
A147993: Sequence S such that 1 is in S and if x is in S, then 6x-1 and 6x+1 are in S.
A237424: Numbers of the form (10^a + 10^b + 1)/3.
A254143: Products of any two not necessarily distinct terms of A237424.
A256292: Numbers which have only digits 6 and 7 in base 10.
A278784: Numbers n such that A000041(n) is of the form 2^7 * k for odd k.

Number of the day: 6826

Marius Sophus Lie was born on this day 174 years ago.

Properties of the number 6826:

6826 = 2 × 3413 is semiprime and squarefree.
6826 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 3412 totatives.
6826 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 6826 results in a sphenic number.
6826 is the difference of 2 positive pentagonal numbers in 2 ways.
6826 = 51² + 65² is the sum of 2 positive squares in 1 way.
6826 = 24² + 25² + 75² is the sum of 3 positive squares.
6826² = 1624² + 6630² is the sum of 2 positive squares in 1 way.
6826² is the sum of 3 positive squares.
6826 is a divisor of 1471⁴ - 1.
6826 is an emirpimes in (at least) the following bases: 4, 5, 6, 7, 8, 11, 14, 15, 18, 22, 29, 30, 36, 42, 44, 46, 49, 51, 54, 55, 56, 57, 59, 63, 69, 70, 73, 78, 80, 84, 86, 89, 91, and 98.
6826 is palindromic in (at least) the following bases: 65, 75, -4, -8, and -91.
6826 in base 4 = 1222222 and consists of only the digits '1' and '2'.
6826 in base 16 = 1aaa and consists of only the digits '1' and 'a'.
6826 in base 27 = 99m and consists of only the digits '9' and 'm'.

The number 6826 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A004250: Number of partitions of n into 3 or more parts.
A020989: (5*4^n-2)/3.
A041227: Denominators of continued fraction convergents to sqrt(125).
A061547: Number of 132 and 213-avoiding derangements of {1,2,...,n}.
A081254: Numbers n such that A081252(m)/m^2 has a local maximum for m = n.
A084170: a(n) = 5*2^n/3 + (-1)^n/3 - 1.
A084214: Inverse binomial transform of a math magic problem.
A112739: Array counting nodes in rooted trees of height n in which the root and internal nodes have valency k (and the leaf nodes have valency one).
A162316: a(n) = 5n^2 + 20n + 1.
A239481: Number of partitions p of n such that if h = 2*min(p), then h is an (h,2)-separator of p; see Comments.

Number of the day: 231762477490

Properties of the number 231762477490:

231762477490 = 2 × 5 × 23176247749 is a sphenic number and squarefree.
231762477490 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 92704990992 totatives.
231762477490 is the difference of 2 positive pentagonal numbers in 2 ways.
231762477490 = 199921² + 437943² = 102829² + 470307² is the sum of 2 positive squares in 2 ways.
231762477490 = 3056² + 5415² + 481377² is the sum of 3 positive squares.
231762477490² = 151825665008² + 175108005006² = 139057486494² + 185409981992² = 96722397006² + 210614871008² = 48991005000² + 226525335010² is the sum of 2 positive squares in 4 ways.
231762477490² is the sum of 3 positive squares.
231762477490 is a divisor of 71^1931353979 - 1.
231762477490 = '231' + '762477490' is the concatenation of 2 sphenic numbers.

Number of the day: 2396

János Bolyai was born on this day 214 years ago.

Properties of the number 2396:

2396 = 2² × 599 is the 2039^th composite number and is not squarefree.
2396 has 2 distinct prime factors, 6 divisors, 3 antidivisors and 1196 totatives.
2396 has an oblong digit sum 20 in base 10.
2396 = 600² - 598² is the difference of 2 nonnegative squares in 1 way.
2396 is the difference of 2 positive pentagonal numbers in 1 way.
2396 is not the sum of 3 positive squares.
2396² is the sum of 3 positive squares.
2396 is a divisor of 421¹³ - 1.
2396 is palindromic in (at least) the following bases: 23, -15, -26, -38, and -42.
2396 in base 7 = 6662 and consists of only the digits '2' and '6'.
2396 in base 18 = 772 and consists of only the digits '2' and '7'.
2396 in base 22 = 4kk and consists of only the digits '4' and 'k'.
2396 in base 23 = 4c4 and consists of only the digits '4' and 'c'.
2396 in base 34 = 22g and consists of only the digits '2' and 'g'.
2396 in base 48 = 11i and consists of only the digits '1' and 'i'.

The number 2396 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006999: Partitioning integers to avoid arithmetic progressions of length 3.
A028875: n^2 - 5.
A054126: Odd-index Fibonacci row-sum array: T(n,k)=U(2n+1,n+1+k), 0<=k<=n, n >= 0, U the array in A054125.
A113789: Numbers n such that n, n+1 and n+2 are products of exactly 3 primes.
A143995: Years in which there are five Thursdays in the month of February, in the Gregorian calendar.
A144798: Integers having ideal digital mean to base 3.
A209973: Number of 2 X 2 matrices having all elements in {0,1,...,n} and determinant 2.
A229644: Cogrowth function of the group Baumslag-Solitar(2,2).
A256089: Non-palindromic balanced numbers in base 9.
A265057: Coordination sequence for (2,3,7) tiling of hyperbolic plane.

Number of the day: 34387030

Properties of the number 34387030:

34387030 = 2 × 5 × 113 × 30431 is the 32275558^th composite number and is squarefree.
34387030 has 4 distinct prime factors, 16 divisors, 13 antidivisors and 13632640 totatives.
34387030 has a triangular digit sum 28 in base 10.
34387030 is the sum of 2 positive triangular numbers.
34387030 is the difference of 2 positive pentagonal numbers in 4 ways.
34387030 = 10² + 243² + 5859² is the sum of 3 positive squares.
34387030² = 16797912² + 30004966² = 4564650² + 34082720² = 24101352² + 24527386² = 20632218² + 27509624² is the sum of 2 positive squares in 4 ways.
34387030² is the sum of 3 positive squares.
34387030 is a divisor of 223⁵⁶⁰ - 1.
34387030 is palindromic in (at least) base -49.

Number of the day: 2534

George Pólya was born on this day 129 years ago.

Properties of the number 2534:

2534 = 2 × 7 × 181 is a sphenic number and squarefree.
2534 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 1080 totatives.
2534 has a semiprime digit sum 14 in base 10.
2534 has a triangular digit product 120 in base 10.
2534 = 5² + 22² + 45² is the sum of 3 positive squares.
2534² = 266² + 2520² is the sum of 2 positive squares in 1 way.
2534² is the sum of 3 positive squares.
2534 is a divisor of 953³ - 1.
2534 = '25' + '34' is the concatenation of 2 semiprime numbers.
2534 is palindromic in (at least) the following bases: 19, 23, and -19.
2534 in base 13 = 11cc and consists of only the digits '1' and 'c'.
2534 in base 18 = 7ee and consists of only the digits '7' and 'e'.
2534 in base 19 = 707 and consists of only the digits '0' and '7'.
2534 in base 20 = 66e and consists of only the digits '6' and 'e'.
2534 in base 22 = 554 and consists of only the digits '4' and '5'.
2534 in base 23 = 4i4 and consists of only the digits '4' and 'i'.
2534 in base 35 = 22e and consists of only the digits '2' and 'e'.

The number 2534 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003349: Numbers that are the sum of 4 positive 5th powers.
A026816: Number of partitions of n in which the greatest part is 10.
A035515: Zeckendorf expansion of n: repeatedly subtract the largest Fibonacci number you can until nothing remains.
A051989: Discriminants of real quadratic fields with class number 2 and related continued fraction period length of 24.
A060920: Bisection of Fibonacci triangle A037027: even indexed members of column sequences of A037027 (not counting leading zeros).
A082260: a(n) = n-th multiple of n with digit sum n.
A143702: a(n) = minimal values of A007947(m(2^n-m))
A238864: Number of partitions of n where the difference between consecutive parts is at most 4.
A251088: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the absolute difference of its antidiagonal elements
A260927: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00010101 00101011 or 01010101

Number of the day: 24717

Properties of the number 24717:

24717 = 3 × 7 × 11 × 107 is the 21980^th composite number and is squarefree.
24717 has 4 distinct prime factors, 16 divisors, 17 antidivisors and 12720 totatives.
24717 has a semiprime digit sum 21 in base 10.
24717 has a Fibonacci digit sum 21 in base 10.
24717 has a triangular digit sum 21 in base 10.
24717 = 12359² - 12358² = 4121² - 4118² = 1769² - 1762² = 1129² - 1118² = 599² - 578² = 391² - 358² = 199² - 122² = 169² - 62² is the difference of 2 nonnegative squares in 8 ways.
24717 is the sum of 2 positive triangular numbers.
24717 is the difference of 2 positive pentagonal numbers in 3 ways.
24717 = 13² + 38² + 152² is the sum of 3 positive squares.
24717² is the sum of 3 positive squares.
24717 is a divisor of 857⁶ - 1.
24717 is palindromic in (at least) the following bases: 30, 38, and 45.
24717 in base 30 = rdr and consists of only the digits 'd' and 'r'.
24717 in base 38 = H4H and consists of only the digits '4' and 'H'.
24717 in base 44 = CXX and consists of only the digits 'C' and 'X'.
24717 in base 45 = C9C and consists of only the digits '9' and 'C'.

The number 24717 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A056858: Triangle of number of rises in restricted growth strings (RGS) for the set partitions of n.
A138691: Numbers of the form 68+p^2 (where p is a prime).
A247345: a(1) = 16. For n > 1, a(n) is the position of the first occurrence of a(n-1) after the decimal point in the decimal expansion of Pi.

Number of the day: 160006

Properties of the number 160006:

160006 = 2 × 7 × 11 × 1039 is the 145321^th composite number and is squarefree.
160006 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 62280 totatives.
160006 has an emirp digit sum 13 in base 10.
160006 has a Fibonacci digit sum 13 in base 10.
Reversing the decimal digits of 160006 results in a sphenic number.
160006 is the sum of 2 positive triangular numbers.
160006 is the difference of 2 positive pentagonal numbers in 4 ways.
160006 = 9² + 74² + 393² is the sum of 3 positive squares.
160006² is the sum of 3 positive squares.
160006 is a divisor of 307³⁴⁶ - 1.
160006 is palindromic in (at least) the following bases: 92, 94, and -82.

Number of the day: 8110

Carl Gustav Jacob Jacobi was born on this day 212 years ago.

Properties of the number 8110:

8110 = 2 × 5 × 811 is a sphenic number and squarefree.
8110 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 3240 totatives.
8110 has a semiprime digit sum 10 in base 10.
8110 has a triangular digit sum 10 in base 10.
8110 is the sum of 2 positive triangular numbers.
8110 is the difference of 2 positive pentagonal numbers in 2 ways.
8110 = 10² + 21² + 87² is the sum of 3 positive squares.
8110² = 4866² + 6488² is the sum of 2 positive squares in 1 way.
8110² is the sum of 3 positive squares.
8110 is a divisor of 1621² - 1.
8110 is palindromic in (at least) the following bases: 42, and -17.
8110 in base 9 = 12111 and consists of only the digits '1' and '2'.
8110 in base 17 = 1b11 and consists of only the digits '1' and 'b'.
8110 in base 22 = gge and consists of only the digits 'e' and 'g'.
8110 in base 41 = 4XX and consists of only the digits '4' and 'X'.
8110 in base 42 = 4P4 and consists of only the digits '4' and 'P'.

The number 8110 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A070938: Harshad numbers which terminate in their digital sum.
A099834: Maximum number of different determinants that can be produced by permuting the elements of a 3 X 3 integer matrix with nonnegative entries <= n.
A101860: (3+n)*(2+33*n+n^2)/6.
A125527: Number of semiprimes <= 2^n.
A141208: a(n) = prime(prime(prime(n) - 1) - 1) - 1, where prime(n) = n-th prime.
A152728: a(n)+a(n+1)+a(n+2)=n^3.
A158271: 324n^2 + 2n.
A158492: 100n^2 + 10.
A206436: Total sum of even parts in the last section of the set of partitions of n.
A255764: Partial sums of A255743.

Number of the day: 193129374941924

Properties of the number 193129374941924:

193129374941924 = 2² × 17 × 5849 × 485576657 is composite and not squarefree.
193129374941924 has 4 distinct prime factors, 24 divisors, 19 antidivisors and 90868873097216 totatives.
Reversing the decimal digits of 193129374941924 results in a sphenic number.
193129374941924 = 48282343735482² - 48282343735480² = 2840137866810² - 2840137866776² = 8254809018² - 8254797320² = 485676090² - 485477224² is the difference of 2 nonnegative squares in 4 ways.
193129374941924 is the difference of 2 positive pentagonal numbers in 4 ways.
193129374941924 = 5303768² + 12845210² = 3148390² + 13535768² = 8838118² + 10724600² = 3591782² + 13424920² is the sum of 2 positive squares in 4 ways.
193129374941924 = 8402² + 38372² + 13897044² is the sum of 3 positive squares.
193129374941924² = 90884411737376² + 170408272007580² = 25065467034340² + 191495895067776² = 85865491410624² + 172991539822820² = 85231753227040² + 173304655757724² = 31348842461924² + 190568112604800² = 136256027502560² + 136869464946276² = 80130601863360² + 175721490178276² = 36904715378076² + 189570560605600² = 96438772014880² + 167327579070876² = 117339855162780² + 153395938198624² = 6350643979776² + 193024933069540² = 56646691421980² + 184635066594624² = 112232303885724² + 157171452337760² is the sum of 2 positive squares in 13 ways.
193129374941924² is the sum of 3 positive squares.
193129374941924 is a divisor of 43^4127401576 - 1.

Number of the day: 3223

Jacques Salomon Hadamard was born on this day 151 years ago.

Julia Robinson was born on this day 97 years ago.

Properties of the number 3223:

3223 = 11 × 293 is semiprime and squarefree.
3223 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 2920 totatives.
3223 has a semiprime digit sum 10 in base 10.
3223 has a triangular digit sum 10 in base 10.
3223 has a triangular digit product 36 in base 10.
3223 = 1612² - 1611² = 152² - 141² is the difference of 2 nonnegative squares in 2 ways.
3223 is the sum of 2 positive triangular numbers.
3223 is the difference of 2 positive pentagonal numbers in 2 ways.
3223 is not the sum of 3 positive squares.
3223² = 748² + 3135² is the sum of 2 positive squares in 1 way.
3223² is the sum of 3 positive squares.
3223 is a divisor of 1759² - 1.
3223 = '3' + '223' is the concatenation of 2 prime numbers.
3223 is an emirpimes in (at least) the following bases: 3, 4, 6, 7, 8, 11, 12, 13, 17, 22, 23, 26, 29, 31, 32, 36, 37, 40, 43, 45, 46, 49, 51, 53, 54, 58, 63, 64, 65, 67, 68, 69, 71, 74, 77, 78, 79, 81, 83, 84, 85, 86, 89, 90, 91, 93, and 97.
3223 is a palindrome (in base 10).
3223 is palindromic in (at least) the following bases: -29, and -35.
3223 consists of only the digits '2' and '3'.
3223 in base 28 = 433 and consists of only the digits '3' and '4'.
3223 in base 56 = 11V and consists of only the digits '1' and 'V'.

The number 3223 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A024786: Number of 2's in all partitions of n.
A032810: Numbers using only digits 2 and 3.
A046328: Palindromes with exactly 2 prime factors (counted with multiplicity).
A056524: Palindromes with even number of digits.
A069910: Expansion of Product_{i in A069908} 1/(1-x^i).
A118595: Palindromes in base 4 (written in base 4).
A118596: Palindromes in base 5 (written in base 5).
A137411: Weak Goodstein sequence starting at 11.
A202616: T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 001 and 010 in rows and columns
A207442: T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically

Number of the day: 6934549294

Properties of the number 6934549294:

6934549294 = 2 × 47 × 619 × 119179 is the 6613632928^th composite number and is squarefree.
6934549294 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 3387992184 totatives.
6934549294 has a semiprime digit sum 55 in base 10.
6934549294 has a Fibonacci digit sum 55 in base 10.
6934549294 has a triangular digit sum 55 in base 10.
6934549294 is the sum of 2 positive triangular numbers.
6934549294 is the difference of 2 positive pentagonal numbers in 4 ways.
6934549294 = 813² + 910² + 83265² is the sum of 3 positive squares.
6934549294² is the sum of 3 positive squares.
6934549294 is a divisor of 1237⁹¹³⁶⁹⁸ - 1.
6934549294 = '693454929' + '4' is the concatenation of 2 semiprime numbers.
6934549294 = '693454' + '9294' is the concatenation of 2 sphenic numbers.

Number of the day: 49928

Properties of the number 49928:

49928 = 2³ × 79² is the 44801^th composite number and is not squarefree.
49928 has 2 distinct prime factors, 12 divisors, 26 antidivisors and 24648 totatives.
Reversing the decimal digits of 49928 results in a sphenic number.
49928 = 12483² - 12481² = 6243² - 6239² = 237² - 79² is the difference of 2 nonnegative squares in 3 ways.
49928 = 158² + 158² is the sum of 2 positive squares in 1 way.
49928 = 10² + 48² + 218² is the sum of 3 positive squares.
49928² is the sum of 3 positive squares.
49928 is a divisor of 491²⁶ - 1.
49928 is palindromic in (at least) the following bases: 38, 59, 78, and -80.
49928 in base 38 = YLY and consists of only the digits 'L' and 'Y'.
49928 in base 39 = WW8 and consists of only the digits '8' and 'W'.
49928 in base 40 = V88 and consists of only the digits '8' and 'V'.
49928 in base 58 = Emm and consists of only the digits 'E' and 'm'.
49928 in base 59 = EKE and consists of only the digits 'E' and 'K'.

The number 49928 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A134507: Number of rectangles in a pyramid built with squares. The squares counted in A092498 are excluded.
A149233: Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (0, 1, -1), (1, 0, -1), (1, 1, 1)}
A166987: Members of A143610 for which both neighbors are squarefree.
A181274: T(n,k)=Number of nXk binary matrices M with rows in strictly increasing order and rows of M*Mtranspose (mod 2) in strictly decreasing order
A181279: Number of 3Xn binary matrices M with rows in strictly increasing order and rows of M*Mtranspose (mod 2) in strictly decreasing order
A188484: Numbers n (other than powers of 2) such that abs(abundance(n)) is an odd square.

Number of the day: 50521760

Properties of the number 50521760:

50521760 = 2⁵ × 5 × 19 × 16619 is the 47491233^th composite number and is not squarefree.
50521760 has 4 distinct prime factors, 48 divisors, 15 antidivisors and 19143936 totatives.
50521760 has an emirpimes digit sum 26 in base 10.
50521760 is the difference of 2 nonnegative squares in 16 ways.
50521760 is the difference of 2 positive pentagonal numbers in 3 ways.
50521760 = 100² + 464² + 7092² is the sum of 3 positive squares.
50521760² = 30313056² + 40417408² is the sum of 2 positive squares in 1 way.
50521760² is the sum of 3 positive squares.
50521760 is a divisor of 569⁴⁷⁴⁸ - 1.

Number of the day: 9824198521655

Properties of the number 9824198521655:

9824198521655 = 5 × 7 × 239 × 1174440947 is composite and squarefree.
9824198521655 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 6708406683552 totatives.
9824198521655 has a semiprime digit sum 65 in base 10.
9824198521655 = 4912099260828² - 4912099260827² = 982419852168² - 982419852163² = 701728465836² - 701728465829² = 140345693184² - 140345693149² = 20552716692² - 20552716453² = 4110543912² - 4110542717² = 2936103204² - 2936101531² = 587224656² - 587216291² is the difference of 2 nonnegative squares in 8 ways.
9824198521655 is the difference of 2 positive pentagonal numbers in 8 ways.
9824198521655 is not the sum of 3 positive squares.
9824198521655² = 5894519112993² + 7859358817324² is the sum of 2 positive squares in 1 way.
9824198521655² is the sum of 3 positive squares.
9824198521655 is a divisor of 1657^803979708 - 1.
9824198521655 = '982' + '4198521655' is the concatenation of 2 emirpimes.
9824198521655 = '98241985' + '21655' is the concatenation of 2 sphenic numbers.

Number of the day: 88566360628

Properties of the number 88566360628:

88566360628 = 2² × 22141590157 is composite and not squarefree.
88566360628 has 2 distinct prime factors, 6 divisors, 69 antidivisors and 44283180312 totatives.
88566360628 has an emirpimes digit sum 58 in base 10.
88566360628 = 22141590158² - 22141590156² is the difference of 2 nonnegative squares in 1 way.
88566360628 is the sum of 2 positive triangular numbers.
88566360628 is the difference of 2 positive pentagonal numbers in 1 way.
88566360628 = 202268² + 218298² is the sum of 2 positive squares in 1 way.
88566360628 = 1674² + 3476² + 297576² is the sum of 3 positive squares.
88566360628² = 6741672980² + 88309399728² is the sum of 2 positive squares in 1 way.
88566360628² is the sum of 3 positive squares.
88566360628 is a divisor of 1051^6631204 - 1.

Number of the day: 2621

Properties of the number 2621:

2621 is the 381^th prime.
2621 has 7 antidivisors and 2620 totatives.
2621 has a prime digit sum 11 in base 10.
Reversing the decimal digits of 2621 results in a semiprime.
2621 = 1311² - 1310² is the difference of 2 nonnegative squares in 1 way.
2621 is the sum of 2 positive triangular numbers.
2621 is the difference of 2 positive pentagonal numbers in 1 way.
2621 = 11² + 50² is the sum of 2 positive squares in 1 way.
2621 = 11² + 14² + 48² is the sum of 3 positive squares.
2621² = 1100² + 2379² is the sum of 2 positive squares in 1 way.
2621² is the sum of 3 positive squares.
2621 is a divisor of 761¹⁰ - 1.
2621 = '26' + '21' is the concatenation of 2 semiprime numbers.
2621 is an emirp in (at least) the following bases: 3, 5, 7, 11, 12, 13, 19, 21, 25, 26, 29, 31, 37, 41, 42, 43, 45, 47, 51, 53, 55, 58, 60, 69, 70, 71, 81, 84, 88, 90, 93, 94, 95, and 99.
2621 is palindromic in (at least) the following bases: 15, -10, -24, and -34.
2621 in base 15 = b9b and consists of only the digits '9' and 'b'.
2621 in base 25 = 44l and consists of only the digits '4' and 'l'.
2621 in base 29 = 33b and consists of only the digits '3' and 'b'.

The number 2621 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007641: Primes of form 2n^2+29.
A096700: Balanced primes of order eight.
A099970: Write 1/e as a binary fraction; read this from left to right and whenever a 1 appears, note the integer formed by reading leftwards from that 1. Then divide these numbers by 2.
A107132: Primes of the form 2x^2+13y^2.
A117876: Primes p=prime(k) of level (1,2), i.e. such that A118534(k) = prime(k-2).
A124575: Triangle read by rows: row n is the first row of the matrix M[n]^(n-1), where M[n] is the n X n tridiagonal matrix with main diagonal (2,4,4,...) and super- and subdiagonals (1,1,1,...).
A141881: Primes congruent to 1 mod 20.
A164288: Members of A164368 which are not Ramanujan primes.
A164294: Primes prime(k) such that all integers in [(prime(k-1)+1)/2,(prime(k)-1)/2] are composite, excluding those primes in A080359.
A261718: Number A(n,k) of partitions of n where each part i is marked with a word of length i over a k-ary alphabet whose letters appear in alphabetical order; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Number of the day: 882600

Nikolai Lobachevsky was born on this day 224 years ago.

Properties of the number 882600:

882600 = 2³ × 3 × 5² × 1471 is the 812582^th composite number and is not squarefree.
882600 has 4 distinct prime factors, 48 divisors, 15 antidivisors and 235200 totatives.
882600 is the difference of 2 nonnegative squares in 12 ways.
882600 is the sum of 2 positive triangular numbers.
882600 is the difference of 2 positive pentagonal numbers in 2 ways.
882600 = 80² + 202² + 914² is the sum of 3 positive squares.
882600² = 529560² + 706080² = 247128² + 847296² is the sum of 2 positive squares in 2 ways.
882600² is the sum of 3 positive squares.
882600 is a divisor of 251⁶ - 1.
882600 is palindromic in (at least) the following bases: 74, and -97.