Number of the day: 882

René Descartes was born on this day 423 years ago.

Properties of the number 882:

882 = 2 × 3² × 7² is the 729^th composite number and is not squarefree.
882 has 3 distinct prime factors, 18 divisors, 12 antidivisors and 252 totatives.
882 = 3³ + 7³ + 8³ is the sum of 3 positive cubes in 1 way.
882 is the sum of 2 positive triangular numbers.
882 = 21² + 21² is the sum of 2 positive squares in 1 way.
882 = 4² + 5² + 29² is the sum of 3 positive squares.
882² is the sum of 3 positive squares.
882 is a proper divisor of 197² - 1.
882 is palindromic in (at least) the following bases: 12, 20, 41, 48, 62, 97, and -22.
882 consists of only the digits '2' and '8'.
882 in base 12 = 616 and consists of only the digits '1' and '6'.
882 in base 19 = 288 and consists of only the digits '2' and '8'.
882 in base 20 = 242 and consists of only the digits '2' and '4'.
882 in base 21 = 200 and consists of only the digits '0' and '2'.
882 in base 29 = 11c and consists of only the digits '1' and 'c'.

The number 882 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000982: a(n) = ceiling(n^2/2).
A001105: a(n) = 2*n^2.
A002088: Sum of totient function: a(n) = Sum_{k=1..n} phi(k), cf. A000010.
A007590: a(n) = floor(n^2/2).
A014574: Average of twin prime pairs.
A028982: Squares and twice squares.
A046746: Sum of smallest parts of all partitions of n.
A276086: Digits in primorial base representation of n become the exponents of successive primes that are multiplied together: a(0)=1, a(n) = A053669(n)*a(A276151(n)).
A299256: Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 3.6.3.6 2D tiling (cf. A008579).
A299267: Partial sums of A299266.

Number of the day: 6801

Stefan Banach was born on this day 127 years ago.

Properties of the number 6801:

6801 is a cyclic number.
6801 = 3 × 2267 is semiprime and squarefree.
6801 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 4532 totatives.
6801 has an emirpimes digit sum 15 in base 10.
6801 has a triangular digit sum 15 in base 10.
Reversing the decimal digits of 6801 results in a sphenic number.
6801 = (18 × 19)/2 + … + (35 × 36)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6801 = 3401² - 3400² = 1135² - 1132² is the difference of 2 nonnegative squares in 2 ways.
6801 is the sum of 2 positive triangular numbers.
6801 is the difference of 2 positive pentagonal numbers in 1 way.
6801 = 1² + 20² + 80² is the sum of 3 positive squares.
6801² is the sum of 3 positive squares.
6801 is a proper divisor of 1153¹¹ - 1.
6801 is an emirpimes in (at least) the following bases: 15, 17, 20, 21, 23, 34, 39, 46, 48, 51, 57, 64, 69, 73, 75, 78, 79, 81, 82, 86, 87, 89, 93, 96, 97, and 98.
6801 is palindromic in (at least) the following bases: 19, 68, 80, -85, and -100.
6801 in base 19 = ifi and consists of only the digits 'f' and 'i'.
6801 in base 47 = 33X and consists of only the digits '3' and 'X'.

The number 6801 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A004126: a(n) = n*(7*n^2 - 1)/6.
A006889: Exponent of least power of 2 having n consecutive 0's in its decimal representation.
A020439: Numbers n such that continued fraction for sqrt(n) has period 100.
A046489: Sum of the first n palindromes (A002113).
A124811: Number of 4-ary Lyndon words of length n with exactly three 1s.
A124814: Triangle of number of 4-ary Lyndon words of length n containing exactly k 1s.
A126587: a(n) = number of integer lattice points inside the right-angle triangle with legs 3n and 4n (and hypotenuse 5n).
A242788: Numbers n such that (n^n-3)/(n-3) is an integer.
A257352: G.f.: (1-2*x+51*x^2)/(1-x)^3.
A260147: G.f.: (1/2) * Sum_{n=-oo..+oo} x^n * (1 + x^n)^n, an even function.

Number of the day: 382457

Properties of the number 382457:

382457 is a cyclic number.
382457 is the 32477^th prime.
382457 has 9 antidivisors and 382456 totatives.
382457 has a prime digit sum 29 in base 10.
382457 has sum of divisors equal to 382458 which is a sphenic number.
Reversing the decimal digits of 382457 results in an emirp.
382457 = 191229² - 191228² is the difference of 2 nonnegative squares in 1 way.
382457 is the sum of 2 positive triangular numbers.
382457 is the difference of 2 positive pentagonal numbers in 1 way.
382457 = 376² + 491² is the sum of 2 positive squares in 1 way.
382457 = 20² + 51² + 616² is the sum of 3 positive squares.
382457² = 99705² + 369232² is the sum of 2 positive squares in 1 way.
382457² is the sum of 3 positive squares.
382457 is a proper divisor of 2⁴⁷⁸⁰⁷ - 1.
382457 = '3' + '82457' is the concatenation of 2 prime numbers.
382457 is an emirp in (at least) the following bases: 5, 6, 7, 10, 21, 23, 35, 51, 70, 80, 87, 89, 91, 92, and 96.
382457 is palindromic in (at least) base 90.

Number of the day: 6000

Alexander Grothendieck was born on this day 91 years ago.

Properties of the number 6000:

6000 = 2⁴ × 3 × 5³ is the 5216^th composite number and is not squarefree.
6000 has 3 distinct prime factors, 40 divisors, 13 antidivisors and 1600 totatives.
6000 has a semiprime digit sum 6 in base 10.
6000 has a triangular digit sum 6 in base 10.
6000 has an oblong digit sum 6 in base 10.
6000 = 8³ + 14³ + 14³ is the sum of 3 positive cubes in 1 way.
6000 = (19 × 20)/2 + … + (34 × 35)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6000 is the difference of 2 nonnegative squares in 12 ways.
6000 is the sum of 2 positive triangular numbers.
6000 is the difference of 2 positive pentagonal numbers in 1 way.
6000 is not the sum of 3 positive squares.
6000² = 3600² + 4800² = 1680² + 5760² = 2112² + 5616² is the sum of 2 positive squares in 3 ways.
6000² is the sum of 3 positive squares.
6000 is a proper divisor of 751² - 1.
6000 = '600' + '0' is the concatenation of 2 oblong numbers.
6000 is palindromic in (at least) the following bases: 79, 99, and -28.
6000 in base 3 = 22020020 and consists of only the digits '0' and '2'.
6000 consists of only the digits '0' and '6'.
6000 in base 14 = 2288 and consists of only the digits '2' and '8'.
6000 in base 20 = f00 and consists of only the digits '0' and 'f'.
6000 in base 24 = aa0 and consists of only the digits '0' and 'a'.
6000 in base 27 = 866 and consists of only the digits '6' and '8'.

The number 6000 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006933: 'Eban' numbers (the letter 'e' is banned!).
A018834: Numbers k such that decimal expansion of k^2 contains k as a substring.
A030283: a(0) = 0; for n>0, a(n) is the smallest number greater than a(n-1) which does not use any digit used by a(n-1).
A037124: Numbers that contain only one nonzero digit.
A057088: Scaled Chebyshev U-polynomials evaluated at i*sqrt(5)/2. Generalized Fibonacci sequence.
A084647: Hypotenuses for which there exist exactly 3 distinct integer triangles.
A132269: Product{k>=0, 1+floor(n/2^k)}.
A134605: Composite numbers such that the square root of the sum of squares of their prime factors (with multiplicity) is an integer.
A238556: Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 7 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=2*floor(n/3), read by rows.
A256633: Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 6 as largest digit.

Number of the day: 575380

Properties of the number 575380:

575380 = 2² × 5 × 13 × 2213 is the 528147^th composite number and is not squarefree.
575380 has 4 distinct prime factors, 24 divisors, 11 antidivisors and 212352 totatives.
575380 has a triangular digit sum 28 in base 10.
575380 = (291 × 292)/2 + … + (303 × 304)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
575380 = 143846² - 143844² = 28774² - 28764² = 11078² - 11052² = 2278² - 2148² is the difference of 2 nonnegative squares in 4 ways.
575380 is the sum of 2 positive triangular numbers.
575380 is the difference of 2 positive pentagonal numbers in 4 ways.
575380 = 348² + 674² = 62² + 756² = 404² + 642² = 126² + 748² is the sum of 2 positive squares in 4 ways.
575380 = 180² + 242² + 696² is the sum of 3 positive squares.
575380² = 304876² + 487968² = 93744² + 567692² = 333172² + 469104² = 175380² + 548000² = 48880² + 573300² = 265620² + 510400² = 383084² + 429312² = 188496² + 543628² = 248948² + 518736² = 345228² + 460304² = 141632² + 557676² = 292116² + 495712² = 221300² + 531120² is the sum of 2 positive squares in 13 ways.
575380² is the sum of 3 positive squares.
575380 is a proper divisor of 1093²⁸ - 1.

Number of the day: 3667

Paul Erös was born on this day 106 years ago.

Properties of the number 3667:

3667 is a cyclic number.
3667 = 19 × 193 is semiprime and squarefree.
3667 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 3456 totatives.
3667 has a semiprime digit sum 22 in base 10.
3667 has an oblong digit product 756 in base 10.
Reversing the decimal digits of 3667 results in an emirpimes.
3667 = 1834² - 1833² = 106² - 87² is the difference of 2 nonnegative squares in 2 ways.
3667 is the sum of 2 positive triangular numbers.
3667 is the difference of 2 positive pentagonal numbers in 2 ways.
3667 = 11² + 39² + 45² is the sum of 3 positive squares.
3667² = 1805² + 3192² is the sum of 2 positive squares in 1 way.
3667² is the sum of 3 positive squares.
3667 is a proper divisor of 277³ - 1.
3667 is an emirpimes in (at least) the following bases: 2, 3, 5, 6, 8, 10, 11, 16, 18, 20, 22, 27, 29, 31, 32, 34, 36, 37, 39, 40, 41, 43, 51, 53, 54, 55, 56, 64, 66, 67, 70, 71, 72, 77, 79, 82, 89, 91, 94, and 98.
3667 is palindromic in (at least) the following bases: 17, 47, -33, -78, and -94.
3667 in base 17 = cbc and consists of only the digits 'b' and 'c'.
3667 in base 46 = 1XX and consists of only the digits '1' and 'X'.
3667 in base 47 = 1V1 and consists of only the digits '1' and 'V'.
3667 in base 60 = 117 and consists of only the digits '1' and '7'.

The number 3667 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007442: Inverse binomial transform of primes.
A078414: a(n) = (a(n-1)+a(n-2))/7^k, where 7^k is the highest power of 7 dividing a(n-1)+a(n-2).
A087886: Numbers n such that 29^n + 2 is prime.
A088405: a(n) = A052217(n)/3.
A114736: Number of planar partitions of n where parts strictly decrease along each row and column.
A147875: Second heptagonal numbers: a(n) = n*(5*n+3)/2.
A227523: Values of n such that L(20) and N(20) are both prime, where L(k) = (n^2+n+1)*2^(2*k) + (2*n+1)*2^k + 1, N(k) = (n^2+n+1)*2^k + n.
A237424: Numbers of the form (10^a + 10^b + 1)/3.
A264351: The x member of the positive proper fundamental solution (x = x2(n), y = y2(n)) of the second class for the Pell equation x^2 - D(n)*y^2 = +8 for odd D(n) = A263012(n).
A303084: T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Number of the day: 822925

Properties of the number 822925:

822925 = 5² × 32917 is the 757281^th composite number and is not squarefree.
822925 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 658320 totatives.
822925 has a triangular digit sum 28 in base 10.
822925 = 117³ - 92³ is the difference of 2 positive cubes in 1 way.
822925 = 411463² - 411462² = 82295² - 82290² = 16471² - 16446² is the difference of 2 nonnegative squares in 3 ways.
822925 is the difference of 2 positive pentagonal numbers in 3 ways.
822925 = 478² + 771² = 243² + 874² = 330² + 845² is the sum of 2 positive squares in 3 ways.
822925 = 8² + 45² + 906² is the sum of 3 positive squares.
822925² = 493755² + 658340² = 149480² + 809235² = 83085² + 818720² = 557700² + 605125² = 424764² + 704827² = 230419² + 790008² = 365957² + 737076² is the sum of 2 positive squares in 7 ways.
822925² is the sum of 3 positive squares.
822925 is a proper divisor of 101⁶³³ - 1.
822925 is palindromic in (at least) base -16.

Number of the day: 710257

Joseph Liouville was born on this day 210 years ago.

Properties of the number 710257:

710257 is a cyclic number.
710257 is the 57319^th prime.
710257 has 13 antidivisors and 710256 totatives.
710257 has a semiprime digit sum 22 in base 10.
710257 has sum of divisors equal to 710258 which is a sphenic number.
Reversing the decimal digits of 710257 results in a sphenic number.
710257 = 355129² - 355128² is the difference of 2 nonnegative squares in 1 way.
710257 is the difference of 2 positive pentagonal numbers in 1 way.
710257 = 519² + 664² is the sum of 2 positive squares in 1 way.
710257 = 39² + 56² + 840² is the sum of 3 positive squares.
710257² = 171535² + 689232² is the sum of 2 positive squares in 1 way.
710257² is the sum of 3 positive squares.
710257 is a proper divisor of 859²⁴ - 1.
710257 is an emirp in (at least) the following bases: 13, 14, 19, 26, 39, 41, 61, 72, 73, 74, 77, 80, and 91.

The number 710257 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A160363: Numerator of Hermite(n, 5/32).

Number of the day: 883622

Pierre-Simon Laplace was born on this day 270 years ago.

Emmy Noether was born on this day 137 years ago.

Properties of the number 883622:

883622 = 2 × 441811 is semiprime and squarefree.
883622 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 441810 totatives.
883622 has a prime digit sum 29 in base 10.
883622 = 26² + 35² + 939² is the sum of 3 positive squares.
883622² is the sum of 3 positive squares.
883622 is a proper divisor of 127⁴⁹⁰⁹ - 1.
883622 is an emirpimes in (at least) the following bases: 2, 6, 13, 16, 17, 20, 23, 26, 34, 46, 48, 56, 62, 72, 78, 79, 80, 83, 88, 90, and 96.

Number of the day: 29092

Properties of the number 29092:

29092 = 2² × 7 × 1039 is the 25929^th composite number and is not squarefree.
29092 has 3 distinct prime factors, 12 divisors, 19 antidivisors and 12456 totatives.
29092 has a semiprime digit sum 22 in base 10.
29092 = 7274² - 7272² = 1046² - 1032² is the difference of 2 nonnegative squares in 2 ways.
29092 is the difference of 2 positive pentagonal numbers in 2 ways.
29092 = 16² + 90² + 144² is the sum of 3 positive squares.
29092² is the sum of 3 positive squares.
29092 is a proper divisor of 113¹⁷³ - 1.
29092 = '2909' + '2' is the concatenation of 2 prime numbers.
29092 is a palindrome (in base 10).
29092 is palindromic in (at least) the following bases: 3, and -96.

The number 29092 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006392: Number of planar maps with n edges and without faces of degree 1 or 2.
A007633: Palindromic in bases 3 and 10.
A100955: Consider all (2n+1)-digit palindromic primes of the form 30...0M0...03 (so that M is a palindrome with <= 2n-1 digits); a(n) = smallest such M.
A109759: Palindromic admirable numbers.
A129210: Largest number not the sum of n distinct nonzero squares.
A138131: Palindromic cyclops numbers.
A162571: Palindromes which are sums of two consecutive primes.
A177722: Number of line segments connecting exactly 6 points in an n x n grid of points
A190397: Number of ways to place 5 nonattacking grasshoppers on a chessboard of size n x n.
A289121: a(n) = (8 - 2*n + 11*n^2 - 6*n^3 + n^4)/4.

Number of the day: 620406

Properties of the number 620406:

620406 = 2 × 3³ × 11489 is the 569762^th composite number and is not squarefree.
620406 has 3 distinct prime factors, 16 divisors, 19 antidivisors and 206784 totatives.
620406 is the sum of 2 positive triangular numbers.
620406 is the difference of 2 positive pentagonal numbers in 2 ways.
620406 = 26² + 149² + 773² is the sum of 3 positive squares.
620406² = 293706² + 546480² is the sum of 2 positive squares in 1 way.
620406² is the sum of 3 positive squares.
620406 is a proper divisor of 5¹⁴⁴ - 1.

Number of the day: 83792

Properties of the number 83792:

83792 = 2⁴ × 5237 is the 75616^th composite number and is not squarefree.
83792 has 2 distinct prime factors, 10 divisors, 17 antidivisors and 41888 totatives.
83792 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 83792 results in a semiprime.
83792 = 20949² - 20947² = 10476² - 10472² = 5241² - 5233² is the difference of 2 nonnegative squares in 3 ways.
83792 is the difference of 2 positive pentagonal numbers in 1 way.
83792 = 56² + 284² is the sum of 2 positive squares in 1 way.
83792 = 8² + 28² + 288² is the sum of 3 positive squares.
83792² = 31808² + 77520² is the sum of 2 positive squares in 1 way.
83792² is the sum of 3 positive squares.
83792 is a proper divisor of 1873²² - 1.
83792 is palindromic in (at least) the following bases: 55, 87, and -47.
83792 in base 14 = 22772 and consists of only the digits '2' and '7'.
83792 in base 30 = 3332 and consists of only the digits '2' and '3'.
83792 in base 55 = RcR and consists of only the digits 'R' and 'c'.

The number 83792 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A019592: From George Gilbert's marks problem: jumping 3 marks at a time (initial positions).
A131188: Indices of products of twin primes in the semiprimes.
A205336: Number of length n+1 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than 3.
A205341: T(n,k)=Number of length n+1 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than k
A273322: Wiener index of graphs of fcc unit cells in a line = Sum of distances in face-centered cubic grid unit cells connected in a row.

Number of the day: 6822871525

Properties of the number 6822871525:

6822871525 = 5² × 53 × 5149337 is the 6506884412^th composite number and is not squarefree.
6822871525 has 3 distinct prime factors, 12 divisors, 17 antidivisors and 5355309440 totatives.
6822871525 has a semiprime digit sum 46 in base 10.
6822871525 = 3411435763² - 3411435762² = 682287155² - 682287150² = 136457443² - 136457418² = 64366739² - 64366686² = 12873475² - 12873210² = 2575331² - 2574006² is the difference of 2 nonnegative squares in 6 ways.
6822871525 is the difference of 2 positive pentagonal numbers in 6 ways.
6822871525 = 48655² + 66750² = 30970² + 76575² = 24207² + 78974² = 21169² + 79842² = 42678² + 70721² = 1126² + 82593² is the sum of 2 positive squares in 6 ways.
6822871525 = 1079² + 1890² + 82572² is the sum of 3 positive squares.
6822871525² = 3943401915² + 5567868280² = 2644128660² + 6289686755² = 1077838480² + 6737198235² = 4743055500² + 4904589725² = 1658509125² + 6618226600² = 2088253475² + 6495442500² = 3445272208² + 5889114981² = 3180048157² + 6036461676² = 185999436² + 6820335773² = 4299475805² + 5297743260² = 2226662720² + 6449306085² = 851690565² + 6769505080² = 3823447236² + 5650913827² = 260934688² + 6817880091² = 3380350596² + 5926618403² = 4093722915² + 5458297220² = 2471681760² + 6359431195² = 592173755² + 6797124840² = 3604535900² + 5793004125² = 4552013908² + 5082395619² = 1910404027² + 6549956664² = 1838313309² + 6570554012² is the sum of 2 positive squares in 22 ways.
6822871525² is the sum of 3 positive squares.
6822871525 is a proper divisor of 257^1556776 - 1.

Number of the day: 9589

Properties of the number 9589:

9589 is a cyclic number.
9589 = 43 × 223 is semiprime and squarefree.
9589 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 9324 totatives.
9589 has an emirp digit sum 31 in base 10.
9589 has a triangular digit product 3240 in base 10.
Reversing the decimal digits of 9589 results in a prime.
9589 = 4795² - 4794² = 133² - 90² is the difference of 2 nonnegative squares in 2 ways.
9589 is the sum of 2 positive triangular numbers.
9589 is the difference of 2 positive pentagonal numbers in 2 ways.
9589 = 7² + 18² + 96² is the sum of 3 positive squares.
9589² is the sum of 3 positive squares.
9589 is a proper divisor of 853⁶ - 1.
9589 = '9' + '589' is the concatenation of 2 semiprime numbers.
9589 is an emirpimes in (at least) the following bases: 7, 11, 12, 13, 14, 15, 16, 20, 21, 29, 32, 35, 39, 41, 47, 49, 50, 54, 59, 60, 61, 63, 70, 78, 79, 80, 81, 82, 84, 87, 95, and 99.
9589 is palindromic in (at least) the following bases: 22, 45, 94, -28, and -31.
9589 in base 3 = 111011011 and consists of only the digits '0' and '1'.
9589 in base 6 = 112221 and consists of only the digits '1' and '2'.
9589 in base 22 = jhj and consists of only the digits 'h' and 'j'.
9589 in base 27 = d44 and consists of only the digits '4' and 'd'.
9589 in base 29 = bbj and consists of only the digits 'b' and 'j'.
9589 in base 30 = ajj and consists of only the digits 'a' and 'j'.
9589 in base 44 = 4ff and consists of only the digits '4' and 'f'.
9589 in base 45 = 4X4 and consists of only the digits '4' and 'X'.
9589 in base 56 = 33D and consists of only the digits '3' and 'D'.

The number 9589 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A031818: Period of continued fraction for sqrt(n) contains exactly 50 ones.
A032402: Numbers k such that 105*2^k+1 is prime.
A077948: Expansion of 1/(1-x-x^2+2*x^3).
A077971: Expansion of 1/(1+x-x^2-2*x^3).
A092119: EULER transform of A001511.
A108753: Difference between the n-th partial sum of the squares (A000330) and the n-th partial sum of the primes (A007504).
A118255: a(1)=1, then a(n)=2*a(n-1) if n is prime, a(n)=2*a(n-1)+1 if n not prime.
A158790: Odd integers n such that (x^n + 1/x^n)/sqrt(8) + 1 is prime, where x = sqrt(8) + sqrt(7).
A194431: a(n) = 8*n^2 - 6*n - 1.
A283394: a(n) = 3*n*(3*n + 7)/2 + 4.

Number of the day: 4448

Properties of the number 4448:

4448 = 2⁵ × 139 is the 3843^th composite number and is not squarefree.
4448 has 2 distinct prime factors, 12 divisors, 13 antidivisors and 2208 totatives.
4448 has an oblong digit sum 20 in base 10.
4448 = 1113² - 1111² = 558² - 554² = 282² - 274² = 147² - 131² is the difference of 2 nonnegative squares in 4 ways.
4448 = 8² + 28² + 60² is the sum of 3 positive squares.
4448² is the sum of 3 positive squares.
4448 is a proper divisor of 97⁶ - 1.
4448 is palindromic in (at least) the following bases: 35, 39, -23, -24, and -57.
4448 in base 3 = 20002202 and consists of only the digits '0' and '2'.
4448 in base 6 = 32332 and consists of only the digits '2' and '3'.
4448 consists of only the digits '4' and '8'.
4448 in base 18 = dd2 and consists of only the digits '2' and 'd'.
4448 in base 22 = 944 and consists of only the digits '4' and '9'.
4448 in base 23 = 899 and consists of only the digits '8' and '9'.
4448 in base 34 = 3ss and consists of only the digits '3' and 's'.
4448 in base 35 = 3m3 and consists of only the digits '3' and 'm'.
4448 in base 38 = 332 and consists of only the digits '2' and '3'.
4448 in base 39 = 2a2 and consists of only the digits '2' and 'a'.

The number 4448 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000938: Number of collinear point-triples in an n X n grid.
A001100: Triangle read by rows: T(n,k) = number of permutations of length n with exactly k rising or falling successions, for n >= 1, 0 <= k <= n-1.
A128129: Expansion of (chi(-q^3)/ chi^3(-q) -1)/3 in powers of q where chi() is a Ramanujan theta function.
A135110: Positive numbers such that the digital sum base 2 and the digital sum base 10 are in a ratio of 2:10.
A164617: Expansion of (phi^3(q^3) / phi(q)) * (psi(-q^3) / psi^3(-q)) in powers of q where phi(), psi() are Ramanujan theta functions.
A178740: Product of the 5th power of a prime (A050997) and a different prime (p^5*q).
A233682: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having the sum of the squares of the edge differences equal to 6 (6 maximizes T(1,1))
A289501: Number of enriched p-trees of weight n.
A292734: Numbers in which 4 outnumbers all other digits together.
A320067: Expansion of Product_{k>0} theta_3(q^k), where theta_3() is the Jacobi theta function.

Number of the day: 18879

Properties of the number 18879:

18879 = 3 × 7 × 29 × 31 is the 16729^th composite number and is squarefree.
18879 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 10080 totatives.
18879 has a semiprime digit sum 33 in base 10.
18879 has an oblong digit product 4032 in base 10.
18879 = 30² + … + 43² = 8² + … + 38² is the sum of at least 2 consecutive positive squares in 2 ways.
18879 = 9440² - 9439² = 3148² - 3145² = 1352² - 1345² = 460² - 439² = 340² - 311² = 320² - 289² = 152² - 65² = 148² - 55² is the difference of 2 nonnegative squares in 8 ways.
18879 is the sum of 2 positive triangular numbers.
18879 is the difference of 2 positive pentagonal numbers in 3 ways.
18879 is not the sum of 3 positive squares.
18879² = 13020² + 13671² is the sum of 2 positive squares in 1 way.
18879² is the sum of 3 positive squares.
18879 is a proper divisor of 347⁶ - 1.
18879 is palindromic in (at least) the following bases: 78, -36, and -56.
18879 in base 6 = 223223 and consists of only the digits '2' and '3'.
18879 in base 35 = fee and consists of only the digits 'e' and 'f'.

The number 18879 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A015636: Number of ordered quadruples of integers from [ 1,n ] with no common factors between pairs.
A060578: Number of homeomorphically irreducible general graphs on 3 labeled node and with n edges.
A062681: Numbers that are sums of 2 or more consecutive squares in more than 1 way.
A130014: Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+881)^2 = y^2.
A130052: Numbers that are the sum of one or more consecutive squares in more than one way.
A138693: Numbers of the form 110 + p^2. (where p is a prime).
A262408: Positive integers m such that pi(m^2) = pi(j^2) + pi(k^2) for no 0 < j <= k < m.
A304469: Number of nX5 0..1 arrays with every element unequal to 0, 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero.
A304470: Number of nX6 0..1 arrays with every element unequal to 0, 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero.
A304472: T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero.

Number of the day: 3010

Properties of the number 3010:

3010 = 2 × 5 × 7 × 43 is the 2578^th composite number and is squarefree.
3010 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 1008 totatives.
3010 has a semiprime digit sum 4 in base 10.
3010 is the sum of 2 positive triangular numbers.
3010 is the difference of 2 positive pentagonal numbers in 5 ways.
3010 = 3² + 20² + 51² is the sum of 3 positive squares.
3010² = 1806² + 2408² is the sum of 2 positive squares in 1 way.
3010² is the sum of 3 positive squares.
3010 is a proper divisor of 601² - 1.
3010 is palindromic in (at least) the following bases: 9, 19, 31, 32, 51, 69, 85, -21, -47, and -59.
3010 in base 3 = 11010111 and consists of only the digits '0' and '1'.
3010 in base 9 = 4114 and consists of only the digits '1' and '4'.
3010 in base 19 = 868 and consists of only the digits '6' and '8'.
3010 in base 20 = 7aa and consists of only the digits '7' and 'a'.
3010 in base 24 = 55a and consists of only the digits '5' and 'a'.
3010 in base 30 = 3aa and consists of only the digits '3' and 'a'.
3010 in base 31 = 343 and consists of only the digits '3' and '4'.
3010 in base 32 = 2u2 and consists of only the digits '2' and 'u'.
3010 in base 50 = 1AA and consists of only the digits '1' and 'A'.
3010 in base 51 = 181 and consists of only the digits '1' and '8'.

The number 3010 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000041: a(n) is the number of partitions of n (the partition numbers).
A000566: Heptagonal numbers (or 7-gonal numbers): n(5n-3)/2.
A035363: Number of partitions of n into even parts.
A035928: Numbers n such that BCR(n) = n, where BCR = binary-complement-and-reverse = take one's complement then reverse bit order.
A052001: Even partition numbers.
A052218: Numbers whose sum of digits is 4.
A059845: a(n) = n*(3*n + 11)/2.
A100039: Positions of occurrences of the natural numbers as fourth subsequence in A100035.
A121030: Multiples of 10 containing a 10 in their decimal representation.
A139063: Numbers k for which (6+k!)/6 is prime.

Number of the day: 47822

Properties of the number 47822:

47822 = 2 × 23911 is semiprime and squarefree.
47822 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 23910 totatives.
47822 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 47822 results in an emirpimes.
47822 = 2² + 27² + 217² is the sum of 3 positive squares.
47822² is the sum of 3 positive squares.
47822 is a proper divisor of 277⁷⁹⁷ - 1.
47822 = '4' + '7822' is the concatenation of 2 semiprime numbers.
47822 is an emirpimes in (at least) the following bases: 2, 5, 6, 10, 13, 14, 15, 16, 17, 20, 21, 24, 26, 28, 29, 30, 31, 36, 37, 41, 47, 52, 56, 57, 68, 69, 70, 73, 78, 79, 80, 85, 88, 90, 93, 96, and 98.
47822 is palindromic in (at least) the following bases: 86, -78, and -99.
47822 in base 37 = YYI and consists of only the digits 'I' and 'Y'.

Number of the day: 867074

Georg Cantor was born on this day 174 years ago.

Properties of the number 867074:

867074 = 2 × 13 × 33349 is a sphenic number and squarefree.
867074 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 400176 totatives.
867074 = (156 × 157)/2 + … + (207 × 208)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
867074 = 257² + 895² = 107² + 925² is the sum of 2 positive squares in 2 ways.
867074 = 12² + 13² + 931² is the sum of 3 positive squares.
867074² = 460030² + 734976² = 333490² + 800376² = 197950² + 844176² = 141960² + 855374² is the sum of 2 positive squares in 4 ways.
867074² is the sum of 3 positive squares.
867074 is a proper divisor of 887⁴² - 1.
867074 = '86707' + '4' is the concatenation of 2 semiprime numbers.

Number of the day: 9010

Properties of the number 9010:

9010 = 2 × 5 × 17 × 53 is the 7890^th composite number and is squarefree.
9010 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 3328 totatives.
9010 has a semiprime digit sum 10 in base 10.
9010 has a triangular digit sum 10 in base 10.
9010 = 1³ + 16³ + 17³ is the sum of 3 positive cubes in 1 way.
9010 = (76 × 77)/2 + … + (78 × 79)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
9010 is the difference of 2 positive pentagonal numbers in 2 ways.
9010 = 63² + 71² = 27² + 91² = 33² + 89² = 19² + 93² is the sum of 2 positive squares in 4 ways.
9010 = 33² + 39² + 80² is the sum of 3 positive squares.
9010² = 4510² + 7800² = 4240² + 7950² = 600² + 8990² = 5874² + 6832² = 1378² + 8904² = 3534² + 8288² = 4914² + 7552² = 3816² + 8162² = 1072² + 8946² = 5406² + 7208² = 3264² + 8398² = 782² + 8976² = 4760² + 7650² is the sum of 2 positive squares in 13 ways.
9010² is the sum of 3 positive squares.
9010 is a proper divisor of 1801² - 1.
9010 is palindromic in (at least) the following bases: 4, 16, 23, 30, 77, 91, -4, -13, -23, -26, -30, and -99.
9010 in base 13 = 4141 and consists of only the digits '1' and '4'.
9010 in base 16 = 2332 and consists of only the digits '2' and '3'.
9010 in base 23 = h0h and consists of only the digits '0' and 'h'.
9010 in base 24 = ffa and consists of only the digits 'a' and 'f'.
9010 in base 25 = eaa and consists of only the digits 'a' and 'e'.
9010 in base 29 = akk and consists of only the digits 'a' and 'k'.
9010 in base 30 = a0a and consists of only the digits '0' and 'a'.

The number 9010 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A032816: Numbers whose set of base 16 digits is {2,3}.
A051870: 18-gonal (or octadecagonal) numbers: a(n) = n*(8*n-7).
A068860: a(1) = 1; a(n+1) is the smallest number > a(n) which differs from it at every digit.
A116295: Numbers n such that n times n+2 gives the concatenation of two numbers m and m+1.
A116555: Anti-Harborth alternating chaotic sequence, 6th type.
A154379: a(n) = 250*n + 10.
A162254: a(n) = (2*n^3 + 5*n^2 + n)/2.
A202962: T(n,k)=Number of arrays of n+2 integers in -k..k with sum zero and adjacent elements differing in absolute value
A212105: Number of (w,x,y,z) with all terms in {1,...,n} and w > harmonic mean of {x,y,z}.
A281877: Numbers that are a primitive sum of two squares in more than 2 ways.