Number of the day: 79196

Pierre Joseph Louis Fatou was born on this day 143 years ago.

Properties of the number 79196:

79196 = 2² × 13 × 1523 is the 71433^th composite number and is not squarefree.
79196 has 3 distinct prime factors, 12 divisors, 7 antidivisors and 36528 totatives.
Reversing the decimal digits of 79196 results in a prime.
79196 = 19800² - 19798² = 1536² - 1510² is the difference of 2 nonnegative squares in 2 ways.
79196 is the difference of 2 positive pentagonal numbers in 2 ways.
79196 is not the sum of 3 positive squares.
79196² = 30460² + 73104² is the sum of 2 positive squares in 1 way.
79196² is the sum of 3 positive squares.
79196 is a proper divisor of 157⁷⁶¹ - 1.
79196 is palindromic in (at least) base 44.
79196 in base 44 = ede and consists of only the digits 'd' and 'e'.

The number 79196 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A041484: Numerators of continued fraction convergents to sqrt(259).
A140746: Numbers n such that n^2 + 3 is powerful, (i.e., is of the form a^2*b^3, with a>=1, b>=1).
A217873: 4*n*(n^2+2)/3.

Number of the day: 3770

L. E. J. Brouwer was born on this day 140 years ago.

Luitzen Egbertus Jan Brouwer was born on this day 140 years ago.

Joseph Leo Doob was born on this day 111 years ago.

Properties of the number 3770:

3770 = 2 × 5 × 13 × 29 is the 3244^th composite number and is squarefree.
3770 has 4 distinct prime factors, 16 divisors, 13 antidivisors and 1344 totatives.
3770 has an emirp digit sum 17 in base 10.
3770 is the difference of 2 positive pentagonal numbers in 3 ways.
3770 = 31² + 53² = 17² + 59² = 37² + 49² = 7² + 61² is the sum of 2 positive squares in 4 ways.
3770 = 11² + 20² + 57² is the sum of 3 positive squares.
3770² = 2262² + 3016² = 624² + 3718² = 442² + 3744² = 2006² + 3192² = 928² + 3654² = 1848² + 3286² = 1914² + 3248² = 1032² + 3626² = 854² + 3672² = 1520² + 3450² = 1450² + 3480² = 1350² + 3520² = 2600² + 2730² is the sum of 2 positive squares in 13 ways.
3770² is the sum of 3 positive squares.
3770 is a proper divisor of 521² - 1.
3770 = '377' + '0' is the concatenation of 2 Fibonacci numbers.
3770 is palindromic in (at least) the following bases: 12, 17, 64, -17, -20, and -22.
3770 in base 4 = 322322 and consists of only the digits '2' and '3'.
3770 in base 8 = 7272 and consists of only the digits '2' and '7'.
3770 in base 12 = 2222 and consists of only the digit '2'.
3770 in base 17 = d0d and consists of only the digits '0' and 'd'.
3770 in base 18 = bb8 and consists of only the digits '8' and 'b'.
3770 in base 19 = a88 and consists of only the digits '8' and 'a'.
3770 in base 21 = 8bb and consists of only the digits '8' and 'b'.

The number 3770 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006039: Primitive non-deficient numbers.
A008892: Aliquot sequence starting at 276.
A022266: a(n) = n*(9*n - 1)/2.
A050381: Number of series-reduced planted trees with n leaves of 2 colors.
A071395: Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers).
A083209: Numbers with exactly one subset of their sets of divisors such that the complement has the same sum.
A097102: Numbers n that are the hypotenuse of exactly 13 distinct integer-sided right triangles, i.e., n^2 can be written as a sum of two squares in 13 ways.
A249551: Numbers k such that there are precisely 8 groups of order k.
A319254: Array read by antidiagonals: T(n,k) is the number of series-reduced rooted trees with n leaves of k colors.
A326627: Sum of all the parts in the partitions of n into 10 squarefree parts.

Number of the day: 51381

Properties of the number 51381:

51381 = 3³ × 11 × 173 is the 46125^th composite number and is not squarefree.
51381 has 3 distinct prime factors, 16 divisors, 15 antidivisors and 30960 totatives.
51381 has a triangular digit product 120 in base 10.
51381 = 6³ + 8³ + 37³ is the sum of 3 positive cubes in 1 way.
51381 = 25691² - 25690² = 8565² - 8562² = 2859² - 2850² = 2341² - 2330² = 965² - 938² = 795² - 762² = 309² - 210² = 235² - 62² is the difference of 2 nonnegative squares in 8 ways.
51381 is the sum of 2 positive triangular numbers.
51381 is the difference of 2 positive pentagonal numbers in 1 way.
51381 = 14² + 89² + 208² is the sum of 3 positive squares.
51381² = 15444² + 49005² is the sum of 2 positive squares in 1 way.
51381² is the sum of 3 positive squares.
51381 is a proper divisor of 439³⁶ - 1.
51381 = '5' + '1381' is the concatenation of 2 prime numbers.
51381 = '51' + '381' is the concatenation of 2 emirpimes.
51381 in base 58 = FFp and consists of only the digits 'F' and 'p'.

The number 51381 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A047068: T(n,n+3), array T as in A047060.
A061422: Numbers k such that 2^(k-1) + k is prime.
A125597: a(1)=1; a(n) = Sum_{1<=k<n, gcd(k,n(n+1)/2)=1} a(k).
A295704: Number of equivalence classes of 132-avoiding permutations of [n], where two permutations are equivalent if they have the same set of pure descents.

Number of the day: 11948159

Properties of the number 11948159:

11948159 is a cyclic number.
11948159 = 199 × 60041 is semiprime and squarefree.
11948159 has 2 distinct prime factors, 4 divisors, 31 antidivisors and 11887920 totatives.
11948159 has a semiprime digit sum 38 in base 10.
Reversing the decimal digits of 11948159 results in an emirpimes.
11948159 = 31³ + 145³ + 207³ is the sum of 3 positive cubes in 1 way.
11948159 = 5974080² - 5974079² = 30120² - 29921² is the difference of 2 nonnegative squares in 2 ways.
11948159 is the sum of 2 positive triangular numbers.
11948159 is the difference of 2 positive pentagonal numbers in 2 ways.
11948159 is not the sum of 3 positive squares.
11948159² = 390040² + 11941791² is the sum of 2 positive squares in 1 way.
11948159² is the sum of 3 positive squares.
11948159 is a proper divisor of 397³¹⁶⁰ - 1.
11948159 is an emirpimes in (at least) the following bases: 3, 5, 6, 8, 10, 14, 19, 24, 26, 29, 32, 37, 38, 41, 44, 45, 48, 49, 50, 53, 56, 61, 66, 68, 70, 71, 74, 76, 80, 83, 91, 92, and 97.

Number of the day: 212154

Properties of the number 212154:

212154 = 2 × 3 × 19 × 1861 is the 193167^th composite number and is squarefree.
212154 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 66960 totatives.
212154 has an emirpimes digit sum 15 in base 10.
212154 has a triangular digit sum 15 in base 10.
212154 = 17² + 92² + 451² is the sum of 3 positive squares.
212154² = 6954² + 212040² is the sum of 2 positive squares in 1 way.
212154² is the sum of 3 positive squares.
212154 is a proper divisor of 1103¹⁰ - 1.
212154 = '21215' + '4' is the concatenation of 2 semiprime numbers.
212154 is palindromic in (at least) the following bases: 61, and -61.
212154 in base 61 = v0v and consists of only the digits '0' and 'v'.

Number of the day: 997751

Properties of the number 997751:

997751 is a cyclic number.
997751 is the 78342^th prime.
997751 has 21 antidivisors and 997750 totatives.
997751 has a semiprime digit sum 38 in base 10.
Reversing the decimal digits of 997751 results in an emirp.
997751 = 498876² - 498875² is the difference of 2 nonnegative squares in 1 way.
997751 is the difference of 2 positive pentagonal numbers in 1 way.
997751 is not the sum of 3 positive squares.
997751² is the sum of 3 positive squares.
997751 is a proper divisor of 1237³⁰⁷ - 1.
997751 = '997' + '751' is the concatenation of 2 prime numbers.
997751 = '9' + '97751' is the concatenation of 2 semiprime numbers.
997751 is an emirp in (at least) the following bases: 2, 3, 5, 10, 16, 28, 34, 35, 39, 64, 73, 75, 86, 87, 88, 90, 96, 97, and 99.

The number 997751 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A061740: Primes with 38 as smallest positive primitive root.

Number of the day: 382038

Frank Plumpton Ramsey was born on this day 118 years ago.

Roy Lee Adler was born on this day 90 years ago.

Properties of the number 382038:

382038 = 2 × 3 × 41 × 1553 is the 349585^th composite number and is squarefree.
382038 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 124160 totatives.
Reversing the decimal digits of 382038 results in a sphenic number.
382038 is the difference of 2 positive pentagonal numbers in 2 ways.
382038 = 37² + 70² + 613² is the sum of 3 positive squares.
382038² = 83862² + 372720² = 39312² + 380010² = 198288² + 326550² = 121770² + 362112² is the sum of 2 positive squares in 4 ways.
382038² is the sum of 3 positive squares.
382038 is a proper divisor of 881⁴⁰ - 1.
382038 = '38' + '2038' is the concatenation of 2 semiprime numbers.
382038 is palindromic in (at least) the following bases: 100, and -95.

The number 382038 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A125130: Successive sums of consecutive primes that form a triangular grid.
A264887: Numbers in A007504 such that omega(a(n)) = Omega(a(n)) = 4.

Number of the day: 486024

Properties of the number 486024:

486024 = 2³ × 3 × 7 × 11 × 263 is the 445577^th composite number and is not squarefree.
486024 has 5 distinct prime factors, 64 divisors, 21 antidivisors and 125760 totatives.
486024 is the difference of 2 nonnegative squares in 16 ways.
486024 is the sum of 2 positive triangular numbers.
486024 is the difference of 2 positive pentagonal numbers in 3 ways.
486024 = 32² + 58² + 694² is the sum of 3 positive squares.
486024² is the sum of 3 positive squares.
486024 is a proper divisor of 1051¹⁰ - 1.
486024 is palindromic in (at least) base 27.
486024 in base 3 = 220200200220 and consists of only the digits '0' and '2'.
486024 in base 27 = oiio and consists of only the digits 'i' and 'o'.

Number of the day: 3009

Axel Thue was born on this day 158 years ago.

Properties of the number 3009:

3009 is a cyclic number.
3009 = 3 × 17 × 59 is a sphenic number and squarefree.
3009 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 1856 totatives.
3009 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 3009 results in a semiprime.
3009 = 1505² - 1504² = 503² - 500² = 97² - 80² = 55² - 4² is the difference of 2 nonnegative squares in 4 ways.
3009 is the sum of 2 positive triangular numbers.
3009 is the difference of 2 positive pentagonal numbers in 1 way.
3009 = 5² + 22² + 50² is the sum of 3 positive squares.
3009² = 1416² + 2655² is the sum of 2 positive squares in 1 way.
3009² is the sum of 3 positive squares.
3009 is a proper divisor of 353⁴ - 1.
3009 is palindromic in (at least) the following bases: 21, 47, 58, -64, and -94.
3009 in base 3 = 11010110 and consists of only the digits '0' and '1'.
3009 in base 21 = 6h6 and consists of only the digits '6' and 'h'.
3009 in base 24 = 559 and consists of only the digits '5' and '9'.
3009 in base 46 = 1JJ and consists of only the digits '1' and 'J'.
3009 in base 47 = 1H1 and consists of only the digits '1' and 'H'.
3009 in base 54 = 11d and consists of only the digits '1' and 'd'.

The number 3009 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000065: -1 + number of partitions of n.
A001402: Number of partitions of n into at most 6 parts.
A007202: Crystal ball sequence for hexagonal close-packing.
A015882: Numbers n such that sigma(n) = sigma(n + 12).
A026812: Number of partitions of n in which the greatest part is 6.
A051876: 24-gonal numbers: a(n) = n*(11*n-10).
A051989: Discriminants of real quadratic fields with class number 2 and related continued fraction period length of 24.
A056105: First spoke of a hexagonal spiral.
A256709: Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 9 as largest digit.
A303814: Generalized 24-gonal (or icositetragonal) numbers: m*(11*m - 10) with m = 0, +1, -1, +2, -2, +3, -3, ...

Number of the day: 692898

Properties of the number 692898:

692898 = 2 × 3 × 23 × 5021 is the 636874^th composite number and is squarefree.
692898 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 220880 totatives.
692898 has a sphenic digit sum 42 in base 10.
692898 has an oblong digit sum 42 in base 10.
692898 is the difference of 2 positive pentagonal numbers in 2 ways.
692898 = 44² + 61² + 829² is the sum of 3 positive squares.
692898² = 212520² + 659502² is the sum of 2 positive squares in 1 way.
692898² is the sum of 3 positive squares.
692898 is a proper divisor of 1723²²⁰ - 1.
692898 is palindromic in (at least) base 18.

The number 692898 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A164246: Number of binary strings of length n with equal numbers of 00101 and 01011 substrings

Number of the day: 661441

Properties of the number 661441:

661441 is a cyclic number.
661441 = 11 × 157 × 383 is a sphenic number and squarefree.
661441 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 595920 totatives.
661441 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 661441 results in a sphenic number.
661441 = 330721² - 330720² = 30071² - 30060² = 2185² - 2028² = 1055² - 672² is the difference of 2 nonnegative squares in 4 ways.
661441 is the sum of 2 positive triangular numbers.
661441 is the difference of 2 positive pentagonal numbers in 3 ways.
661441 = 146² + 309² + 738² is the sum of 3 positive squares.
661441² = 358105² + 556116² is the sum of 2 positive squares in 1 way.
661441² is the sum of 3 positive squares.
661441 is a proper divisor of 1531¹³⁰ - 1.
661441 is palindromic in (at least) base 5.

Number of the day: 210386

Properties of the number 210386:

210386 = 2 × 11 × 73 × 131 is the 191542^th composite number and is squarefree.
210386 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 93600 totatives.
210386 has an oblong digit sum 20 in base 10.
210386 is the sum of 2 positive triangular numbers.
210386 is the difference of 2 positive pentagonal numbers in 3 ways.
210386 = 15² + 56² + 455² is the sum of 3 positive squares.
210386² = 138336² + 158510² is the sum of 2 positive squares in 1 way.
210386² is the sum of 3 positive squares.
210386 is a proper divisor of 173²⁰ - 1.
210386 = '2103' + '86' is the concatenation of 2 semiprime numbers.
210386 in base 60 = wQQ and consists of only the digits 'Q' and 'w'.

The number 210386 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A034536: Multiplicity of highest weight (or singular) vectors associated with character chi_148 of Monster module.

Number of the day: 433193

Galileo Galilei was born on this day 457 years ago.

Alfred North Whitehead was born on this day 160 years ago.

Properties of the number 433193:

433193 is a cyclic number.
433193 is the 36417^th prime.
433193 has 29 antidivisors and 433192 totatives.
433193 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 433193 results in a sphenic number.
433193 = 216597² - 216596² is the difference of 2 nonnegative squares in 1 way.
433193 is the difference of 2 positive pentagonal numbers in 1 way.
433193 = 197² + 628² is the sum of 2 positive squares in 1 way.
433193 = 2² + 15² + 658² is the sum of 3 positive squares.
433193² = 247432² + 355575² is the sum of 2 positive squares in 1 way.
433193² is the sum of 3 positive squares.
433193 is a proper divisor of 1669³⁴⁶ - 1.
433193 = '433' + '193' is the concatenation of 2 prime numbers.
433193 = '4' + '33193' is the concatenation of 2 semiprime numbers.
433193 is an emirp in (at least) the following bases: 3, 8, 12, 15, 19, 27, 28, 29, 45, 50, 59, 62, 64, 71, 77, 78, 84, 92, 93, and 98.

Number of the day: 718238677

Edmund Landau was born on this day 144 years ago.

Properties of the number 718238677:

718238677 = 13² × 107 × 39719 is the 681090903^th composite number and is not squarefree.
718238677 has 3 distinct prime factors, 12 divisors, 47 antidivisors and 656776848 totatives.
718238677 has an emirpimes digit sum 49 in base 10.
Reversing the decimal digits of 718238677 results in a semiprime.
718238677 = 359119339² - 359119338² = 27624571² - 27624558² = 3356309² - 3356202² = 2125051² - 2124882² = 258869² - 257478² = 28901² - 10818² is the difference of 2 nonnegative squares in 6 ways.
718238677 is the difference of 2 positive pentagonal numbers in 5 ways.
718238677 = 56² + 729² + 26790² is the sum of 3 positive squares.
718238677² = 276245645² + 662989548² = 505742027² + 509991960² is the sum of 2 positive squares in 2 ways.
718238677² is the sum of 3 positive squares.
718238677 is a proper divisor of 1499¹¹⁹¹⁵⁴ - 1.
718238677 = '718' + '238677' is the concatenation of 2 semiprime numbers.

Number of the day: 2005

Peter Gustav Lejeune Dirichlet was born on this day 216 years ago.

Properties of the number 2005:

2005 = 5 × 401 is semiprime and squarefree.
2005 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 1600 totatives.
2005 has a prime digit sum 7 in base 10.
Reversing the decimal digits of 2005 results in a sphenic number.
2005 = 1003² - 1002² = 203² - 198² is the difference of 2 nonnegative squares in 2 ways.
2005 is the sum of 2 positive triangular numbers.
2005 is the difference of 2 positive pentagonal numbers in 2 ways.
2005 = 22² + 39² = 18² + 41² is the sum of 2 positive squares in 2 ways.
2005 = 4² + 15² + 42² is the sum of 3 positive squares.
2005² = 1357² + 1476² = 1203² + 1604² = 1037² + 1716² = 200² + 1995² is the sum of 2 positive squares in 4 ways.
2005² is the sum of 3 positive squares.
2005 is a proper divisor of 421⁴ - 1.
2005 is an emirpimes in (at least) the following bases: 4, 5, 6, 7, 8, 9, 15, 17, 19, 21, 22, 23, 27, 31, 32, 33, 34, 35, 37, 40, 41, 42, 44, 45, 46, 48, 49, 52, 53, 54, 55, 59, 61, 67, 69, 73, 74, 75, 78, 79, 84, 87, 91, 93, 94, and 99.
2005 is palindromic in (at least) the following bases: 20, -18, -20, -23, and -26.
2005 in base 4 = 133111 and consists of only the digits '1' and '3'.
2005 in base 12 = 11b1 and consists of only the digits '1' and 'b'.
2005 in base 13 = bb3 and consists of only the digits '3' and 'b'.
2005 in base 14 = a33 and consists of only the digits '3' and 'a'.
2005 in base 19 = 5aa and consists of only the digits '5' and 'a'.
2005 in base 20 = 505 and consists of only the digits '0' and '5'.
2005 in base 22 = 433 and consists of only the digits '3' and '4'.
2005 in base 25 = 355 and consists of only the digits '3' and '5'.
2005 in base 31 = 22l and consists of only the digits '2' and 'l'.
2005 in base 44 = 11P and consists of only the digits '1' and 'P'.

The number 2005 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A014915: a(1)=1, a(n) = n*3^(n-1) + a(n-1).
A050993: 5-Kndel numbers.
A053701: Vertically symmetric numbers.
A098645: List the positions of all digits '1' in the sequence. This is the lexicographically earliest increasing sequence with this property.
A138993: a(n) = Frobenius number for 7 successive primes = F[p(n),p(n+1),p(n+2),p(n+3),p(n+4),p(n+5),p(n+6)].
A177814: Numbers n such that n^3 divides 14^(n^2)+1.
A193842: Triangular array: the fission of the polynomial sequence ((x+1)^n: n >= 0) by the polynomial sequence ((x+2)^n: n >= 0). (Fission is defined at Comments.)
A256631: Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 5 as largest digit.
A292450: Numbers where 0 outnumbers any other digit.
A293880: Numbers having '20' as substring of their digits.

Number of the day: 376

Properties of the number 376:

376 = 2³ × 47 is the 301^th composite number and is not squarefree.
376 has 2 distinct prime factors, 8 divisors, 3 antidivisors and 184 totatives.
Reversing the decimal digits of 376 results in a prime.
376 = 95² - 93² = 49² - 45² is the difference of 2 nonnegative squares in 2 ways.
376 is the difference of 2 positive pentagonal numbers in 1 way.
376 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
376 = (16 × (3 × 16-1))/2 is a pentagonal number.
376 = 4² + 6² + 18² is the sum of 3 positive squares.
376² is the sum of 3 positive squares.
376 is a proper divisor of 281² - 1.
376 is palindromic in (at least) the following bases: 15, 46, 93, -17, -25, and -75.
376 in base 3 = 111221 and consists of only the digits '1' and '2'.
376 in base 13 = 22c and consists of only the digits '2' and 'c'.
376 in base 14 = 1cc and consists of only the digits '1' and 'c'.
376 in base 15 = 1a1 and consists of only the digits '1' and 'a'.

The number 376 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000071: a(n) = Fibonacci(n) - 1.
A000326: Pentagonal numbers: a(n) = n*(3*n-1)/2.
A001318: Generalized pentagonal numbers: m*(3*m - 1)/2, m = 0, +-1, +-2, +-3, ....
A001840: Expansion of x /((1 - x)^2 * (1 - x^3)).
A004207: a(0) = 1, a(n) = sum of digits of all previous terms.
A008590: Multiples of 8.
A014613: Numbers that are products of 4 primes (these numbers are sometimes called "4-almost primes", a generalization of semiprimes).
A033950: Refactorable numbers: number of divisors of n divides n. Also known as tau numbers.
A034856: a(n) = binomial(n+1, 2) + n - 1 = n*(n + 3)/2 - 1.
A329744: Triangle read by rows where T(n,k) is the number of compositions of n > 0 with runs-resistance k, 0 <= k <= n - 1.

Number of the day: 8152

Properties of the number 8152:

8152 is the 1960^th totient number.
8152 = 2³ × 1019 is the 7128^th composite number and is not squarefree.
8152 has 2 distinct prime factors, 8 divisors, 13 antidivisors and 4072 totatives.
Reversing the decimal digits of 8152 results in a semiprime.
8152 = 3³ + 5³ + 20³ is the sum of 3 positive cubes in 1 way.
8152 = 2039² - 2037² = 1021² - 1017² is the difference of 2 nonnegative squares in 2 ways.
8152 is the sum of 2 positive triangular numbers.
8152 is the difference of 2 positive pentagonal numbers in 2 ways.
8152 = 4² + 6² + 90² is the sum of 3 positive squares.
8152² is the sum of 3 positive squares.
8152 is a proper divisor of 17⁵⁰⁹ - 1.
8152 is palindromic in (at least) the following bases: 42, -7, and -13.
8152 in base 41 = 4YY and consists of only the digits '4' and 'Y'.
8152 in base 42 = 4Q4 and consists of only the digits '4' and 'Q'.

The number 8152 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003288: Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,0,2).
A032522: Number of point symmetric solutions to non-attacking queens problem on n X n board.
A050539: Numbers k such that 27*2^k-1 is prime.
A054410: Susceptibility series H_3 for 2-dimensional Ising model (divided by 2).
A054999: Integers that can be expressed as the sum of consecutive primes in exactly 4 ways.
A069125: a(n) = (11*n^2 - 11*n + 2)/2.
A073153: Triangle of numbers relating two sequences A073155 and A073156.
A189890: a(n) = (n^3 - 2*n^2 + 3*n + 2)/2.
A276891: Number T(n,k) of ordered set partitions of [n] where k is minimal such that for each block b the smallest integer interval containing b has at most k elements; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
A302150: T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

Number of the day: 9007250

Properties of the number 9007250:

9007250 = 2 × 5³ × 7 × 5147 is the 8404343^th composite number and is not squarefree.
9007250 has 4 distinct prime factors, 32 divisors, 19 antidivisors and 3087600 totatives.
9007250 has a prime digit sum 23 in base 10.
9007250 = 204² + … + 328² is the sum of at least 2 consecutive positive squares in 1 way.
9007250 is the difference of 2 positive pentagonal numbers in 7 ways.
9007250 = 15² + 32² + 3001² is the sum of 3 positive squares.
9007250² = 5404350² + 7205800² = 2522030² + 8646960² = 3170552² + 8430786² is the sum of 2 positive squares in 3 ways.
9007250² is the sum of 3 positive squares.
9007250 is a proper divisor of 1901⁹³⁰ - 1.
9007250 in base 3 = 121221121121212 and consists of only the digits '1' and '2'.

Number of the day: 389728

Properties of the number 389728:

389728 = 2⁵ × 19 × 641 is the 356685^th composite number and is not squarefree.
389728 has 3 distinct prime factors, 24 divisors, 11 antidivisors and 184320 totatives.
389728 has an emirp digit sum 37 in base 10.
Reversing the decimal digits of 389728 results in a semiprime.
389728 = 18³ + 22³ + 72³ is the sum of 3 positive cubes in 1 way.
389728 = 97433² - 97431² = 48718² - 48714² = 24362² - 24354² = 12187² - 12171² = 5147² - 5109² = 2602² - 2526² = 1358² - 1206² = 793² - 489² is the difference of 2 nonnegative squares in 8 ways.
389728 is the sum of 2 positive triangular numbers.
389728 is the difference of 2 positive pentagonal numbers in 3 ways.
389728 = 120² + 172² + 588² is the sum of 3 positive squares.
389728² = 121600² + 370272² is the sum of 2 positive squares in 1 way.
389728² is the sum of 3 positive squares.
389728 is a proper divisor of 487¹² - 1.
389728 is palindromic in (at least) base 37.
389728 in base 37 = 7PP7 and consists of only the digits '7' and 'P'.

Number of the day: 3657

Daniel Bernoulli was born on this day 321 years ago.

Properties of the number 3657:

3657 is a cyclic number.
3657 = 3 × 23 × 53 is a sphenic number and squarefree.
3657 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 2288 totatives.
3657 has a semiprime digit sum 21 in base 10.
3657 has a Fibonacci digit sum 21 in base 10.
3657 has a triangular digit sum 21 in base 10.
3657 has a triangular digit product 630 in base 10.
Reversing the decimal digits of 3657 results in a semiprime.
3657 = 1829² - 1828² = 611² - 608² = 91² - 68² = 61² - 8² is the difference of 2 nonnegative squares in 4 ways.
3657 is the sum of 2 positive triangular numbers.
3657 is the difference of 2 positive pentagonal numbers in 1 way.
3657 = 2² + 17² + 58² is the sum of 3 positive squares.
3657² = 1932² + 3105² is the sum of 2 positive squares in 1 way.
3657² is the sum of 3 positive squares.
3657 is a proper divisor of 1931⁴ - 1.
3657 is palindromic in (at least) the following bases: 68, -42, and -43.
3657 in base 8 = 7111 and consists of only the digits '1' and '7'.
3657 in base 42 = 233 and consists of only the digits '2' and '3'.

The number 3657 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033816: a(n) = 2*n^2 + 3*n + 3.
A039665: Sets of 4 consecutive numbers with equal number of divisors.
A086381: Numbers n such that p=n^2+2 and p+2 are primes.
A111133: Number of partitions of n into at least two distinct parts.
A135703: a(n) = n*(7*n-2).
A151542: Generalized pentagonal numbers: a(n) = 12*n + 3*n*(n-1)/2.
A179791: Values x for records of minima of positive distance d between a ninth power of positive integer x and a square of integer y such d = x^9 - y^2 (x<>k^2 and y<>k^9).
A302069: T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
A306670: Numbers k with exactly three distinct prime factors and such that cototient(k) is a square.
A319060: A(n, k) is the k-th number b > 1 such that b^(prime(n+i)-1) == 1 (mod prime(n+i)^2) for each i = 0..2, with k running over the positive integers; square array, read by antidiagonals, downwards.

Number of the day: 272021

Godfrey Harold Hardy was born on this day 144 years ago.

Happy e-Day!

Properties of the number 272021:

272021 is a cyclic number.
272021 = 23 × 11827 is semiprime and squarefree.
272021 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 260172 totatives.
272021 has a semiprime digit sum 14 in base 10.
272021 = 136011² - 136010² = 5925² - 5902² is the difference of 2 nonnegative squares in 2 ways.
272021 is the difference of 2 positive pentagonal numbers in 2 ways.
272021 = 10² + 39² + 520² is the sum of 3 positive squares.
272021² is the sum of 3 positive squares.
272021 is a proper divisor of 1889⁹⁹ - 1.
272021 is an emirpimes in (at least) the following bases: 2, 5, 7, 8, 14, 18, 19, 22, 25, 33, 36, 49, 50, 51, 52, 53, 54, 57, 58, 59, 61, 63, 64, 65, 74, 76, 77, 78, 80, 82, 83, 87, 89, and 100.
272021 is palindromic in (at least) base -17.

Number of the day: 27518

Properties of the number 27518:

27518 = 2 × 13759 is semiprime and squarefree.
27518 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 13758 totatives.
27518 has a prime digit sum 23 in base 10.
27518 = 2² + 17² + 165² is the sum of 3 positive squares.
27518² is the sum of 3 positive squares.
27518 is a proper divisor of 5²²⁹³ - 1.
27518 is an emirpimes in (at least) the following bases: 3, 4, 5, 6, 9, 14, 20, 21, 24, 25, 27, 31, 36, 38, 40, 41, 42, 43, 45, 46, 47, 48, 51, 53, 55, 57, 62, 65, 67, 70, 71, 74, 75, 83, 84, 85, 86, 90, 91, 92, 96, and 97.
27518 is palindromic in (at least) the following bases: 52, and 61.
27518 in base 51 = ATT and consists of only the digits 'A' and 'T'.
27518 in base 52 = A9A and consists of only the digits '9' and 'A'.
27518 in base 60 = 7cc and consists of only the digits '7' and 'c'.
27518 in base 61 = 7O7 and consists of only the digits '7' and 'O'.

The number 27518 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A114138: Number of (ordered) sequences of coins (each of which has value 1, 2, 5, 10, 20, 50, 100 or 200) which add to n.
A114140: Number of ordered sequences of coins (each of which has value 1, 2, 5, 10 or 20) which add to n.
A326338: Number of simple graphs with vertices {1..n} whose weakly nesting edges are connected.

Number of the day: 8613

Properties of the number 8613:

8613 = 3³ × 11 × 29 is the 7540^th composite number and is not squarefree.
8613 has 3 distinct prime factors, 16 divisors, 31 antidivisors and 5040 totatives.
8613 has a Fibonacci digit product 144 in base 10.
8613 = 4307² - 4306² = 1437² - 1434² = 483² - 474² = 397² - 386² = 173² - 146² = 163² - 134² = 147² - 114² = 93² - 6² is the difference of 2 nonnegative squares in 8 ways.
8613 is the difference of 2 positive pentagonal numbers in 1 way.
8613 = 7² + 10² + 92² is the sum of 3 positive squares.
8613² = 5940² + 6237² is the sum of 2 positive squares in 1 way.
8613² is the sum of 3 positive squares.
8613 is a proper divisor of 1567⁵ - 1.
8613 = '861' + '3' is the concatenation of 2 triangular numbers.
8613 is palindromic in (at least) the following bases: 25, 98, and -79.
8613 in base 22 = hhb and consists of only the digits 'b' and 'h'.
8613 in base 25 = djd and consists of only the digits 'd' and 'j'.
8613 in base 41 = 553 and consists of only the digits '3' and '5'.
8613 in base 53 = 33R and consists of only the digits '3' and 'R'.

The number 8613 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A067705: a(n) = 11*n^2 + 22*n.
A139273: a(n) = n*(8*n - 3).
A145068: Zero followed by partial sums of A059100, starting at n=1.
A152759: 3 times 9-gonal (or nonagonal) numbers: 3n(7n-5)/2.
A229917: Numbers of espalier polycubes of a given volume in dimension 4.
A230659: Number of n X 5 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).
A230661: T(n,k)=Number of nXk 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j)
A240486: Number of partitions of n containing m(1) as a part, where m denotes multiplicity.
A305342: Number of nX3 0..1 arrays with every element unequal to 0, 1, 3, 5 or 8 king-move adjacent elements, with upper left element zero.
A305532: Expansion of 1/(1 - x/(1 - 1*2*x/(1 - 2*3*x/(1 - 3*4*x/(1 - 4*5*x/(1 - ...)))))), a continued fraction.

Number of the day: 405029

Christopher Zeeman was born on this day 96 years ago.

Properties of the number 405029:

405029 is a cyclic number.
405029 is the 34225^th prime.
405029 has 7 antidivisors and 405028 totatives.
405029 has an oblong digit sum 20 in base 10.
405029 = 202515² - 202514² is the difference of 2 nonnegative squares in 1 way.
405029 is the sum of 2 positive triangular numbers.
405029 is the difference of 2 positive pentagonal numbers in 1 way.
405029 = 130² + 623² is the sum of 2 positive squares in 1 way.
405029 = 82² + 183² + 604² is the sum of 3 positive squares.
405029² = 161980² + 371229² is the sum of 2 positive squares in 1 way.
405029² is the sum of 3 positive squares.
405029 is a proper divisor of 31⁷⁷⁸⁹ - 1.
405029 is an emirp in (at least) the following bases: 2, 3, 4, 11, 15, 29, 31, 43, 49, 50, 53, 69, 70, 71, 80, 94, and 97.
405029 is palindromic in (at least) the following bases: 95, -86, and -88.

Number of the day: 862924910

Gaston Julia was born on this day 128 years ago.

Properties of the number 862924910:

862924910 = 2 × 5 × 61 × 1414631 is the 818715048^th composite number and is squarefree.
862924910 has 4 distinct prime factors, 16 divisors, 55 antidivisors and 339511200 totatives.
862924910 has a prime digit sum 41 in base 10.
862924910 is the difference of 2 positive pentagonal numbers in 4 ways.
862924910 = 11² + 710² + 29367² is the sum of 3 positive squares.
862924910² = 517754946² + 690339928² = 384779632² + 772388526² = 585657234² + 633754688² = 155609410² + 848778600² is the sum of 2 positive squares in 4 ways.
862924910² is the sum of 3 positive squares.
862924910 is a proper divisor of 13³⁴⁶⁴⁴ - 1.

Number of the day: 74892

Jacques Philippe Marie Binet was born on this day 235 years ago.

Bartel Leendert van der Waerden was born on this day 118 years ago.

Properties of the number 74892:

74892 = 2² × 3 × 79² is the 67505^th composite number and is not squarefree.
74892 has 3 distinct prime factors, 18 divisors, 13 antidivisors and 24648 totatives.
74892 has a sphenic digit sum 30 in base 10.
74892 has an oblong digit sum 30 in base 10.
74892 has an oblong digit product 4032 in base 10.
Reversing the decimal digits of 74892 results in a semiprime.
74892 = 18724² - 18722² = 6244² - 6238² = 316² - 158² is the difference of 2 nonnegative squares in 3 ways.
74892 is the sum of 2 positive triangular numbers.
74892 is the difference of 2 positive pentagonal numbers in 1 way.
74892 = 70² + 74² + 254² is the sum of 3 positive squares.
74892² is the sum of 3 positive squares.
74892 is a proper divisor of 491²⁶ - 1.
74892 = '7489' + '2' is the concatenation of 2 prime numbers.
74892 is palindromic in (at least) the following bases: 59, 78, -80, and -97.
74892 in base 59 = LUL and consists of only the digits 'L' and 'U'.

The number 74892 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A142462: Triangle read by rows: T(n,k) (1<=k<=n) given by T(n, 1) = T(n,n) = 1, otherwise T(n, k) = (m*n-m*k+1)*T(n-1,k-1)+(m*k-m+1)*T(n-1,k), where m = 7.
A178455: Partial sums of floor(2^n/7).
A252431: Number of (n+2) X (6+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0, 2, 4, 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0, 2, 4, 6 or 7.
A252433: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 2 4 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 2 4 6 or 7
A252437: Number of (4+2)X(n+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 2 4 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 2 4 6 or 7
A316403: Number of multisets of exactly two nonempty binary words with a total of n letters such that no word has a majority of 0's.

Number of the day: 840631

John Napier was born on this day 471 years ago.

John Napier was born on this day 471 years ago.

Properties of the number 840631:

840631 is a cyclic number.
840631 = 11 × 76421 is semiprime and squarefree.
840631 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 764200 totatives.
840631 has a semiprime digit sum 22 in base 10.
840631 = 420316² - 420315² = 38216² - 38205² is the difference of 2 nonnegative squares in 2 ways.
840631 is the difference of 2 positive pentagonal numbers in 2 ways.
840631 is not the sum of 3 positive squares.
840631² = 166881² + 823900² is the sum of 2 positive squares in 1 way.
840631² is the sum of 3 positive squares.
840631 is a proper divisor of 331³⁸²¹ - 1.
840631 is an emirpimes in (at least) the following bases: 3, 5, 7, 14, 17, 21, 28, 29, 34, 38, 43, 44, 52, 54, 60, 62, 63, 64, 66, 69, 79, 81, 84, 85, and 96.
840631 is palindromic in (at least) base 30.
840631 in base 30 = 11411 and consists of only the digits '1' and '4'.