Number of the day: 7232

René Descartes was born on this day 422 years ago.

Properties of the number 7232:

7232 = 2⁶ × 113 is the 6307^th composite number and is not squarefree.
7232 has 2 distinct prime factors, 14 divisors, 11 antidivisors and 3584 totatives.
7232 has a semiprime digit sum 14 in base 10.
Reversing the decimal digits of 7232 results in a semiprime.
7232 = 1809² - 1807² = 906² - 902² = 456² - 448² = 234² - 218² = 129² - 97² is the difference of 2 nonnegative squares in 5 ways.
7232 = 56² + 64² is the sum of 2 positive squares in 1 way.
7232 = 16² + 24² + 80² is the sum of 3 positive squares.
7232² = 960² + 7168² is the sum of 2 positive squares in 1 way.
7232² is the sum of 3 positive squares.
7232 is a proper divisor of 241⁴ - 1.
7232 is palindromic in (at least) base 15.
7232 in base 15 = 2222 and consists of only the digit '2'.
7232 in base 21 = g88 and consists of only the digits '8' and 'g'.
7232 in base 42 = 448 and consists of only the digits '4' and '8'.

The number 7232 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A030632: Numbers with 14 divisors.
A080054: G.f.: Product_{n >= 0} (1+x^(2n+1))/(1-x^(2n+1)).
A124212: E.g.f.: exp(x)/sqrt(2-exp(2*x)).
A145303: a(n) = ((8 + sqrt(8))^n + (8 - sqrt(8))^n)/2.
A189987: Numbers with prime factorization pq^6.
A197409: T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4
A210030: Expansion of phi(-q) / phi(q^2) in powers of q where phi() is a Ramanujan theta function.
A285828: Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 105", based on the 5-celled von Neumann neighborhood.
A286704: Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 211", based on the 5-celled von Neumann neighborhood.
A287285: Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 260", based on the 5-celled von Neumann neighborhood.

Number of the day: 376043

Stefan Banach was born on this day 126 years ago.

Properties of the number 376043:

376043 is a cyclic number.
376043 = 29 × 12967 is semiprime and squarefree.
376043 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 363048 totatives.
376043 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 376043 results in an emirpimes.
376043 = 188022² - 188021² = 6498² - 6469² is the difference of 2 nonnegative squares in 2 ways.
376043 is the difference of 2 positive pentagonal numbers in 2 ways.
376043 = 7² + 15² + 613² is the sum of 3 positive squares.
376043² = 259340² + 272307² is the sum of 2 positive squares in 1 way.
376043² is the sum of 3 positive squares.
376043 is a proper divisor of 1741²¹⁶¹ - 1.
376043 = '37' + '6043' is the concatenation of 2 prime numbers.
376043 is an emirpimes in (at least) the following bases: 8, 9, 10, 12, 15, 18, 19, 20, 21, 22, 23, 24, 27, 33, 45, 55, 56, 57, 59, 60, 61, 63, 65, 68, 70, 73, 75, 76, 78, 79, 91, 95, 97, 98, and 99.
376043 is palindromic in (at least) the following bases: -86, -93, and -94.

Number of the day: 662309190

Properties of the number 662309190:

662309190 = 2 × 3³ × 5 × 353 × 6949 is the 627909161^th composite number and is not squarefree.
662309190 has 5 distinct prime factors, 64 divisors, 39 antidivisors and 176090112 totatives.
662309190 has a triangular digit sum 36 in base 10.
662309190 is the sum of 2 positive triangular numbers.
662309190 is the difference of 2 positive pentagonal numbers in 3 ways.
662309190 = 641² + 1250² + 25697² is the sum of 3 positive squares.
662309190² = 422151750² + 510334560² = 327841560² + 575476650² = 214151850² + 626731560² = 263676384² + 607559238² = 31520664² + 661558698² = 204717456² + 629876358² = 372894138² + 547360416² = 154976598² + 643922136² = 83012742² + 657086256² = 397385514² + 529847352² = 354858192² + 559221894² = 184081734² + 636213312² = 234462600² + 619419690² is the sum of 2 positive squares in 13 ways.
662309190² is the sum of 3 positive squares.
662309190 is a proper divisor of 311⁶⁹⁴⁸ - 1.

Number of the day: 6285

Alexander Grothendieck was born on this day 90 years ago.

Properties of the number 6285:

6285 is a cyclic number.
6285 = 3 × 5 × 419 is a sphenic number and squarefree.
6285 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 3344 totatives.
6285 has a semiprime digit sum 21 in base 10.
6285 has a Fibonacci digit sum 21 in base 10.
6285 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 6285 results in a sphenic number.
6285 = 3143² - 3142² = 1049² - 1046² = 631² - 626² = 217² - 202² is the difference of 2 nonnegative squares in 4 ways.
6285 is the difference of 2 positive pentagonal numbers in 2 ways.
6285 = 5² + 22² + 76² is the sum of 3 positive squares.
6285² = 3771² + 5028² is the sum of 2 positive squares in 1 way.
6285² is the sum of 3 positive squares.
6285 is a proper divisor of 839² - 1.
6285 = '62' + '85' is the concatenation of 2 emirpimes.
6285 is palindromic in (at least) the following bases: 25, and -61.
6285 in base 24 = all and consists of only the digits 'a' and 'l'.
6285 in base 25 = a1a and consists of only the digits '1' and 'a'.

The number 6285 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A115160: Numbers that are not the sum of two triangular numbers and a fourth power.
A160353: Numbers of the form pqr, where p<q<r are odd primes such that r = +/-1 (mod pq).
A201245: Number of ways to place 4 non-attacking ferses on an n X n board.
A201272: Number of n X 3 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.
A208613: Triangle of coefficients of polynomials v(n,x) jointly generated with A208612; see the Formula section.
A209819: Triangle of coefficients of polynomials u(n,x) jointly generated with A209820; see the Formula section.
A246853: Numbers n such that sigma(n+3) - sigma(n) = n + 3.
A271152: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 299", based on the 5-celled von Neumann neighborhood.
A272782: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 533", based on the 5-celled von Neumann neighborhood.
A278094: T(n,k)=Number of nXk 0..1 arrays with every element both equal and not equal to some elements at offset (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

Number of the day: 683097

Properties of the number 683097:

683097 is a cyclic number.
683097 = 3 × 227699 is semiprime and squarefree.
683097 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 455396 totatives.
683097 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 683097 results in a sphenic number.
683097 = 341549² - 341548² = 113851² - 113848² is the difference of 2 nonnegative squares in 2 ways.
683097 is the difference of 2 positive pentagonal numbers in 1 way.
683097 = 14² + 25² + 826² is the sum of 3 positive squares.
683097² is the sum of 3 positive squares.
683097 is a proper divisor of 577⁶²⁹ - 1.
683097 is an emirpimes in (at least) the following bases: 3, 7, 9, 11, 15, 23, 25, 26, 46, 51, 56, 60, 66, 76, 77, 81, 82, 84, and 99.
683097 in base 42 = 99A9 and consists of only the digits '9' and 'A'.

Number of the day: 336312

Paul Erös was born on this day 105 years ago.

Properties of the number 336312:

336312 = 2³ × 3⁵ × 173 is the 307412^th composite number and is not squarefree.
336312 has 3 distinct prime factors, 48 divisors, 31 antidivisors and 111456 totatives.
336312 = 13³ + 27³ + 68³ = 19³ + 45³ + 62³ is the sum of 3 positive cubes in 2 ways.
336312 is the difference of 2 nonnegative squares in 12 ways.
336312 is the difference of 2 positive pentagonal numbers in 1 way.
336312 = 28² + 38² + 578² is the sum of 3 positive squares.
336312² = 101088² + 320760² is the sum of 2 positive squares in 1 way.
336312² is the sum of 3 positive squares.
336312 is a proper divisor of 971⁸⁶ - 1.

Number of the day: 40514

Properties of the number 40514:

40514 = 2 × 47 × 431 is a sphenic number and squarefree.
40514 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 19780 totatives.
40514 has a semiprime digit sum 14 in base 10.
40514 is the difference of 2 positive pentagonal numbers in 1 way.
40514 = 7² + 8² + 201² is the sum of 3 positive squares.
40514² is the sum of 3 positive squares.
40514 is a proper divisor of 1409¹⁰ - 1.
40514 is palindromic in (at least) the following bases: 61, 82, and -54.
40514 in base 34 = 111k and consists of only the digits '1' and 'k'.
40514 in base 53 = EMM and consists of only the digits 'E' and 'M'.
40514 in base 61 = AsA and consists of only the digits 'A' and 's'.

The number 40514 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A067797: Numbers n such that phi(n)+phi(n+1) = n+2.
A111759: Number of bipartite outerplanar graphs on n unlabeled nodes.
A226648: Numbers n such that sum_{k=1..n} sigma(k) is a triangular number, where sigma(k) = sum of divisors of k (A000203).
A239329: The number of NE partitions of n (see Comments).
A252376: Number of (n+2)X(n+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 3 5 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 3 5 6 or 7

Number of the day: 46016

Joseph Liouville was born on this day 209 years ago.

Properties of the number 46016:

46016 = 2⁶ × 719 is the 41254^th composite number and is not squarefree.
46016 has 2 distinct prime factors, 14 divisors, 3 antidivisors and 22976 totatives.
46016 has an emirp digit sum 17 in base 10.
46016 = 11505² - 11503² = 5754² - 5750² = 2880² - 2872² = 1446² - 1430² = 735² - 703² is the difference of 2 nonnegative squares in 5 ways.
46016 is the difference of 2 positive pentagonal numbers in 1 way.
46016 is not the sum of 3 positive squares.
46016² is the sum of 3 positive squares.
46016 is a proper divisor of 1439² - 1.
46016 = '4601' + '6' is the concatenation of 2 semiprime numbers.
46016 is palindromic in (at least) the following bases: 42, 72, 86, -62, and -81.
46016 in base 42 = Q3Q and consists of only the digits '3' and 'Q'.
46016 in base 61 = CMM and consists of only the digits 'C' and 'M'.

The number 46016 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A036893: Number of partitions of 5n such that cn(0,5) < cn(1,5) = cn(4,5) < cn(2,5) = cn(3,5).
A237632: Number of (n+1)X(3+1) 0..2 arrays with the upper median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one

Number of the day: 503597269

Pierre-Simon Laplace was born on this day 269 years ago.

Emmy Noether was born on this day 136 years ago.

Properties of the number 503597269:

503597269 = 7 × 37 × 113 × 17207 is the 477062229^th composite number and is squarefree.
503597269 has 4 distinct prime factors, 16 divisors, 27 antidivisors and 416247552 totatives.
503597269 has a semiprime digit sum 46 in base 10.
Reversing the decimal digits of 503597269 results in a semiprime.
503597269 = 251798635² - 251798634² = 35971237² - 35971230² = 6805387² - 6805350² = 2228363² - 2228250² = 972325² - 972066² = 318725² - 317934² = 62315² - 58134² = 23237² - 6030² is the difference of 2 nonnegative squares in 8 ways.
503597269 is the sum of 2 positive triangular numbers.
503597269 is the difference of 2 positive pentagonal numbers in 7 ways.
503597269 = 87² + 190² + 22440² is the sum of 3 positive squares.
503597269² = 225119181² + 450479260² = 66849195² + 499140656² = 98647731² + 493840900² = 163328844² + 476375795² is the sum of 2 positive squares in 4 ways.
503597269² is the sum of 3 positive squares.
503597269 is a proper divisor of 677⁷³⁷⁴ - 1.
503597269 = '503' + '597269' is the concatenation of 2 prime numbers.

Number of the day: 419457

Properties of the number 419457:

419457 is a cyclic number.
419457 = 3 × 89 × 1571 is a sphenic number and squarefree.
419457 has 3 distinct prime factors, 8 divisors, 21 antidivisors and 276320 totatives.
419457 has a sphenic digit sum 30 in base 10.
419457 has an oblong digit sum 30 in base 10.
419457 = 209729² - 209728² = 69911² - 69908² = 2401² - 2312² = 919² - 652² is the difference of 2 nonnegative squares in 4 ways.
419457 is the difference of 2 positive pentagonal numbers in 1 way.
419457 = 5² + 46² + 646² is the sum of 3 positive squares.
419457² = 183807² + 377040² is the sum of 2 positive squares in 1 way.
419457² is the sum of 3 positive squares.
419457 is a proper divisor of 179¹⁰ - 1.
419457 = '419' + '457' is the concatenation of 2 prime numbers.
419457 is palindromic in (at least) base -21.

Number of the day: 534890172

Joseph Fourier was born on this day 250 years ago.

George David Birkhoff was born on this day 134 years ago.

Properties of the number 534890172:

534890172 = 2² × 3 × 44574181 is the 506796221^th composite number and is not squarefree.
534890172 has 3 distinct prime factors, 12 divisors, 9 antidivisors and 178296720 totatives.
534890172 has an emirpimes digit sum 39 in base 10.
534890172 = 133722544² - 133722542² = 44574184² - 44574178² is the difference of 2 nonnegative squares in 2 ways.
534890172 is the difference of 2 positive pentagonal numbers in 1 way.
534890172 is not the sum of 3 positive squares.
534890172² = 85290480² + 528046428² is the sum of 2 positive squares in 1 way.
534890172² is the sum of 3 positive squares.
534890172 is a proper divisor of 149²¹²²⁵⁸ - 1.
534890172 = '53489017' + '2' is the concatenation of 2 prime numbers.

Number of the day: 4078

Properties of the number 4078:

4078 = 2 × 2039 is semiprime and squarefree.
4078 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 2038 totatives.
4078 has a prime digit sum 19 in base 10.
4078 is the difference of 2 positive pentagonal numbers in 2 ways.
4078 = 3² + 10² + 63² is the sum of 3 positive squares.
4078² is the sum of 3 positive squares.
4078 is a proper divisor of 3¹⁰¹⁹ - 1.
4078 is an emirpimes in (at least) the following bases: 2, 4, 5, 6, 8, 11, 15, 25, 28, 29, 37, 39, 41, 44, 45, 51, 52, 54, 56, 58, 59, 62, 64, 66, 67, 69, 70, 71, 86, 87, 89, 91, 94, 95, and 98.
4078 is palindromic in (at least) the following bases: 22, 23, -6, -17, and -19.
4078 in base 4 = 333232 and consists of only the digits '2' and '3'.
4078 in base 16 = fee and consists of only the digits 'e' and 'f'.
4078 in base 18 = caa and consists of only the digits 'a' and 'c'.
4078 in base 22 = 898 and consists of only the digits '8' and '9'.
4078 in base 23 = 7g7 and consists of only the digits '7' and 'g'.
4078 in base 28 = 55i and consists of only the digits '5' and 'i'.

The number 4078 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A064092: Generalized Catalan numbers C(9; n).
A085146: Numbers n such that n!!!!+1 is prime.
A096373: Number of partitions of n such that the least part occurs exactly twice.
A121330: Number of bridged bicyclic skeletons with n carbon atoms (see Parks et al. for precise definition).
A196590: T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,2,0,1,4 for x=0,1,2,3,4
A196802: T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,2,0,4,1 for x=0,1,2,3,4
A226441: T(n,k)=Number of permutations of 1..n with fewer than k interior elements having values lying between the values of their neighbors
A239470: Number of 4-separable partitions of n; see Comments.
A254204: T(n,k)=Number of length n 1..(k+2) arrays with no leading or trailing partial sum equal to a prime
A256708: Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 8 as largest digit.

Number of the day: 74010

Properties of the number 74010:

74010 = 2 × 3 × 5 × 2467 is the 66708^th composite number and is squarefree.
74010 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 19728 totatives.
74010 has an oblong digit sum 12 in base 10.
74010 is the sum of 2 positive triangular numbers.
74010 is the difference of 2 positive pentagonal numbers in 2 ways.
74010 = 13² + 20² + 271² is the sum of 3 positive squares.
74010² = 44406² + 59208² is the sum of 2 positive squares in 1 way.
74010² is the sum of 3 positive squares.
74010 is a proper divisor of 1171¹⁸ - 1.
74010 is palindromic in (at least) base -77.
74010 in base 18 = cc7c and consists of only the digits '7' and 'c'.

The number 74010 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A240210: Number of partitions p of n such that median(p) > multiplicity(max(p)).

Number of the day: 49683

Christian Goldbach was born on this day 328 years ago.

Properties of the number 49683:

49683 = 3 × 16561 is semiprime and squarefree.
49683 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 33120 totatives.
49683 has a sphenic digit sum 30 in base 10.
49683 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 49683 results in a sphenic number.
49683 = 24842² - 24841² = 8282² - 8279² is the difference of 2 nonnegative squares in 2 ways.
49683 is the sum of 2 positive triangular numbers.
49683 is the difference of 2 positive pentagonal numbers in 1 way.
49683 = 1² + 29² + 221² is the sum of 3 positive squares.
49683² = 10317² + 48600² is the sum of 2 positive squares in 1 way.
49683² is the sum of 3 positive squares.
49683 is a proper divisor of 421⁵ - 1.
49683 = '4' + '9683' is the concatenation of 2 semiprime numbers.
49683 is an emirpimes in (at least) the following bases: 3, 8, 15, 17, 25, 31, 33, 40, 43, 44, 45, 47, 49, 51, 54, 59, 65, 66, 81, 93, 96, and 98.
49683 is palindromic in (at least) base 87.
49683 in base 45 = OO3 and consists of only the digits '3' and 'O'.

The number 49683 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A025976: Expansion of 1/((1-2x)(1-4x)(1-8x)(1-9x)).
A082865: a(n) is the sum of the preceding terms that are coprime to n.

Number of the day: 55394124603

Properties of the number 55394124603:

55394124603 = 3 × 131 × 140951971 is a sphenic number and squarefree.
55394124603 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 36647512200 totatives.
55394124603 has a sphenic digit sum 42 in base 10.
55394124603 has an oblong digit sum 42 in base 10.
Reversing the decimal digits of 55394124603 results in a sphenic number.
55394124603 = 27697062302² - 27697062301² = 9232354102² - 9232354099² = 211428022² - 211427891² = 70476182² - 70475789² is the difference of 2 nonnegative squares in 4 ways.
55394124603 is the sum of 2 positive triangular numbers.
55394124603 is the difference of 2 positive pentagonal numbers in 2 ways.
55394124603 = 817² + 1217² + 235355² is the sum of 3 positive squares.
55394124603² is the sum of 3 positive squares.
55394124603 is a proper divisor of 1279^1143805 - 1.
55394124603 = '55' + '394124603' is the concatenation of 2 semiprime numbers.

Number of the day: 940270

Properties of the number 940270:

940270 = 2 × 5 × 17 × 5531 is the 866063^th composite number and is squarefree.
940270 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 353920 totatives.
940270 has a semiprime digit sum 22 in base 10.
940270 is the difference of 2 positive pentagonal numbers in 4 ways.
940270 = 110² + 111² + 957² is the sum of 3 positive squares.
940270² = 442480² + 829650² = 143806² + 929208² = 398232² + 851774² = 564162² + 752216² is the sum of 2 positive squares in 4 ways.
940270² is the sum of 3 positive squares.
940270 is a proper divisor of 239¹⁰ - 1.
940270 = '9402' + '70' is the concatenation of 2 sphenic numbers.

The number 940270 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A203889: Number of (n+1)X2 0..4 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing
A203893: Number of (n+1)X6 0..4 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing
A203896: T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing

Number of the day: 3142018

Albert Einstein was born on this day 139 years ago.

Happy π Day!

Properties of the number 3142018:

3142018 = 2 × 11 × 251 × 569 is the 2915718^th composite number and is squarefree.
3142018 has 4 distinct prime factors, 16 divisors, 27 antidivisors and 1420000 totatives.
3142018 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 3142018 results in a sphenic number.
3142018 is the difference of 2 positive pentagonal numbers in 2 ways.
3142018 = 36² + 199² + 1761² is the sum of 3 positive squares.
3142018² = 1275582² + 2871440² is the sum of 2 positive squares in 1 way.
3142018² is the sum of 3 positive squares.
3142018 is a proper divisor of 113³⁵⁵ - 1.
3142018 = '314' + '2018' is the concatenation of 2 emirpimes.

Number of the day: 171

Properties of the number 171:

171 = 3² × 19 is the 131^th composite number and is not squarefree.
171 has 2 distinct prime factors, 6 divisors, 9 antidivisors and 108 totatives.
171 has a semiprime digit sum 9 in base 10.
171 has a prime digit product 7 in base 10.
171 = 86² - 85² = 30² - 27² = 14² - 5² is the difference of 2 nonnegative squares in 3 ways.
171 = (18 × 19)/2 is a triangular number.
171 is the difference of 2 positive pentagonal numbers in 1 way.
171 = 1² + 7² + 11² is the sum of 3 positive squares.
171² is the sum of 3 positive squares.
171 is a proper divisor of 37² - 1.
171 is a palindrome (in base 10).
171 is palindromic in (at least) the following bases: 7, 18, 56, -2, -8, -17, -34, and -85.
171 in base 4 = 2223 and consists of only the digits '2' and '3'.
171 in base 5 = 1141 and consists of only the digits '1' and '4'.
171 in base 6 = 443 and consists of only the digits '3' and '4'.
171 in base 7 = 333 and consists of only the digit '3'.
171 consists of only the digits '1' and '7'.

The number 171 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000217: Triangular numbers: a(n) = binomial(n+1,2) = n(n+1)/2 = 0 + 1 + 2 + ... + n.
A000959: Lucky numbers.
A001045: Jacobsthal sequence (or Jacobsthal numbers): a(n) = a(n-1) + 2*a(n-2), with a(0) = 0, a(1) = 1.
A002113: Palindromes in base 10.
A004767: a(n) = 4*n + 3.
A005349: Niven (or Harshad) numbers: numbers that are divisible by the sum of their digits.
A008585: a(n) = 3*n.
A014105: Second hexagonal numbers: a(n) = n*(2n+1).
A014612: Numbers that are the product of exactly three (not necessarily distinct) primes.
A139250: Toothpick sequence (see Comments lines for definition).

Number of the day: 59840

Properties of the number 59840:

59840 = 2⁶ × 5 × 11 × 17 is the 53792^th composite number and is not squarefree.
59840 has 4 distinct prime factors, 56 divisors, 23 antidivisors and 20480 totatives.
59840 has an emirpimes digit sum 26 in base 10.
59840 is the difference of 2 nonnegative squares in 20 ways.
59840 is the difference of 2 positive pentagonal numbers in 4 ways.
59840 is not the sum of 3 positive squares.
59840² = 28160² + 52800² = 9152² + 59136² = 25344² + 54208² = 35904² + 47872² is the sum of 2 positive squares in 4 ways.
59840² is the sum of 3 positive squares.
59840 is a proper divisor of 353⁴ - 1.
59840 is palindromic in (at least) base -77.

The number 59840 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A011931: [ n(n-1)(n-2)(n-3)/21 ].
A148574: 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, 1), (0, 1, -1), (0, 1, 1), (1, 0, -1)}
A214475: Degrees of irreducible representations of orthogonal group O10-(2).

Number of the day: 97927

Properties of the number 97927:

97927 is a cyclic number.
97927 is the 9412^th prime.
97927 has 21 antidivisors and 97926 totatives.
97927 has a semiprime digit sum 34 in base 10.
97927 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 97927 results in a sphenic number.
97927 = 48964² - 48963² is the difference of 2 nonnegative squares in 1 way.
97927 is the difference of 2 positive pentagonal numbers in 1 way.
97927 is not the sum of 3 positive squares.
97927² is the sum of 3 positive squares.
97927 is a proper divisor of 263⁸⁵⁹ - 1.
97927 is an emirp in (at least) the following bases: 4, 5, 11, 21, 23, 24, 26, 27, 33, 39, 43, 46, 49, 50, 51, 56, 61, 69, 79, 84, 85, and 92.
97927 is palindromic in (at least) the following bases: 91, and -63.
97927 in base 52 = aBB and consists of only the digits 'B' and 'a'.
97927 in base 62 = PTT and consists of only the digits 'P' and 'T'.

The number 97927 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A060110: Numbers in Morse code, with 1 for a dot, 2 for a dash and 0 between digits/letters and then converting from base 3 to base 10.
A236042: Primes p such that 100*p+1, 100*p+3, 100*p+7, and 100*p+9 are all prime.

Number of the day: 772215

Properties of the number 772215:

772215 = 3 × 5 × 51481 is a sphenic number and squarefree.
772215 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 411840 totatives.
Reversing the decimal digits of 772215 results in a semiprime.
772215 = 386108² - 386107² = 128704² - 128701² = 77224² - 77219² = 25748² - 25733² is the difference of 2 nonnegative squares in 4 ways.
772215 is the sum of 2 positive triangular numbers.
772215 is the difference of 2 positive pentagonal numbers in 2 ways.
772215 is not the sum of 3 positive squares.
772215² = 368535² + 678600² = 112332² + 764001² = 321759² + 701988² = 463329² + 617772² is the sum of 2 positive squares in 4 ways.
772215² is the sum of 3 positive squares.
772215 is a proper divisor of 307⁴⁴ - 1.
772215 = '77' + '2215' is the concatenation of 2 semiprime numbers.

Number of the day: 6633253

Properties of the number 6633253:

6633253 is a cyclic number.
6633253 = 11 × 603023 is semiprime and squarefree.
6633253 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 6030220 totatives.
6633253 has a triangular digit sum 28 in base 10.
6633253 = 3316627² - 3316626² = 301517² - 301506² is the difference of 2 nonnegative squares in 2 ways.
6633253 is the sum of 2 positive triangular numbers.
6633253 is the difference of 2 positive pentagonal numbers in 2 ways.
6633253 = 127² + 150² + 2568² is the sum of 3 positive squares.
6633253² is the sum of 3 positive squares.
6633253 is a proper divisor of 1429³¹⁷³⁸ - 1.
6633253 is an emirpimes in (at least) the following bases: 3, 9, 11, 15, 16, 17, 24, 29, 30, 35, 40, 41, 43, 44, 46, 52, 53, 56, 58, 65, 66, 68, 70, 77, 81, 83, 84, 85, 86, 88, 89, 93, 95, and 99.
6633253 is palindromic in (at least) base -54.
6633253 in base 3 = 110111000010001 and consists of only the digits '0' and '1'.

Number of the day: 16128

Properties of the number 16128:

16128 = 2⁸ × 3² × 7 is the 14250^th composite number and is not squarefree.
16128 has 3 distinct prime factors, 54 divisors, 7 antidivisors and 4608 totatives.
16128 = 2³ + 19³ + 21³ is the sum of 3 positive cubes in 1 way.
16128 is the difference of 2 nonnegative squares in 21 ways.
16128 is the sum of 2 positive triangular numbers.
16128 is the difference of 2 positive pentagonal numbers in 2 ways.
16128 is not the sum of 3 positive squares.
16128² is the sum of 3 positive squares.
16128 is a proper divisor of 127² - 1.
16128 is palindromic in (at least) the following bases: 47, 58, -30, -49, and -75.
16128 in base 4 = 3330000 and consists of only the digits '0' and '3'.
16128 in base 46 = 7SS and consists of only the digits '7' and 'S'.
16128 in base 47 = 7E7 and consists of only the digits '7' and 'E'.
16128 in base 48 = 700 and consists of only the digits '0' and '7'.
16128 in base 57 = 4ss and consists of only the digits '4' and 's'.
16128 in base 58 = 4k4 and consists of only the digits '4' and 'k'.

The number 16128 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000056: Order of the group SL(2,Z_n).
A069272: 11-almost primes (generalization of semiprimes).
A079262: Octanacci numbers: a(0)=a(1)=...=a(6)=0, a(7)=1; for n >= 8, a(n) = Sum_{i=1..8} a(n-i).
A084920: a(n) = (prime(n)-1)*(prime(n)+1).
A109906: A triangle of coefficients based on A000045 and the Pascal's triangle: t(n,m)=Fibonacci[(n - m + 1)]*Fibonacci[(m + 1)]*Binomial[n, m].
A173121: a(n) = sinh(2*arccosh(n))^2 = 4*n^2*(n^2-1).
A195092: Numbers n such that (number of prime factors of n counted with multiplicity) less (number of distinct prime factors of n) = 8.
A227499: Number of the Lipschitz quaternions in a reduced system modulo n.
A248882: Expansion of Product_{k>=1} (1+x^k)^(k^3).
A299950: Coefficients in expansion of (E_4^3/E_6^2)^(1/18).

Number of the day: 9394234278254

Properties of the number 9394234278254:

9394234278254 = 2 × 7 × 19 × 73 × 1087 × 445069 is composite and squarefree.
9394234278254 has 6 distinct prime factors, 64 divisors, 43 antidivisors and 3758481762048 totatives.
9394234278254 has an emirpimes digit sum 62 in base 10.
Reversing the decimal digits of 9394234278254 results in a prime.
9394234278254 = 9522² + 12557² + 3064961² is the sum of 3 positive squares.
9394234278254² = 6177030758304² + 7077847743890² = 2415112046270² + 9078483985704² = 1164609617304² + 9321766040510² = 5251934808120² + 7789019093954² is the sum of 2 positive squares in 4 ways.
9394234278254² is the sum of 3 positive squares.
9394234278254 is a proper divisor of 1861²⁵⁴¹²⁴ - 1.
9394234278254 = '939' + '4234278254' is the concatenation of 2 semiprime numbers.

Number of the day: 789

Properties of the number 789:

789 is a cyclic number.
789 = 3 × 263 is semiprime and squarefree.
789 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 524 totatives.
789 has sum of divisors equal to 1056 which is an oblong number.
Reversing the decimal digits of 789 results in a sphenic number.
Reversing the decimal digits of 789 results in a Fibonacci number.
789 = 5² + … + 13² is the sum of at least 2 consecutive positive squares in 1 way.
789 = 395² - 394² = 133² - 130² is the difference of 2 nonnegative squares in 2 ways.
789 is the difference of 2 positive pentagonal numbers in 1 way.
789 = 1² + 2² + 28² is the sum of 3 positive squares.
789² is the sum of 3 positive squares.
789 is a proper divisor of 1051² - 1.
789 = '7' + '89' is the concatenation of 2 prime numbers.
789 is an emirpimes in (at least) the following bases: 4, 6, 7, 8, 16, 17, 19, 20, 21, 23, 26, 27, 28, 29, 35, 39, 44, 46, 55, 60, 61, 65, 66, 71, 73, 75, 77, 85, 86, 89, 90, 93, and 100.
789 in base 6 = 3353 and consists of only the digits '3' and '5'.
789 in base 12 = 559 and consists of only the digits '5' and '9'.

The number 789 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A024199: a(n) = (2n-1)!! * Sum_{k=0..n-1}(-1)^k/(2k+1).
A025328: Numbers that are the sum of 3 nonzero squares in exactly 8 ways.
A025335: Numbers that are the sum of 3 nonzero squares in 7 or more ways.
A033075: Positive numbers n such that all pairs of consecutive decimal digits differ by 1.
A069606: a(1) = 4; a(n) = smallest number such that the juxtaposition a(1)a(2)...a(n) is a prime.
A071148: Partial sums of sequence of odd primes (A065091); a(n) = sum of the first n odd primes.
A091214: Composite numbers whose binary representation encodes a polynomial irreducible over GF(2).
A147562: Number of "ON" cells at n-th stage in the "Ulam-Warburton" two-dimensional cellular automaton.
A186651: Total number of positive integers below 10^n requiring 3 positive biquadrates in their representation as sum of biquadrates.
A299285: Coordination sequence for "tea" 3D uniform tiling.

Number of the day: 27893651751

Georg Cantor was born on this day 173 years ago.

Properties of the number 27893651751:

27893651751 = 3⁴ × 7² × 7027879 is composite and not squarefree.
27893651751 has 3 distinct prime factors, 30 divisors, 33 antidivisors and 15939227304 totatives.
27893651751 is the difference of 2 nonnegative squares in 15 ways.
27893651751 is the sum of 2 positive triangular numbers.
27893651751 is the difference of 2 positive pentagonal numbers in 3 ways.
27893651751 is not the sum of 3 positive squares.
27893651751² is the sum of 3 positive squares.
27893651751 is a proper divisor of 1297^1892121 - 1.
27893651751 = '2' + '7893651751' is the concatenation of 2 prime numbers.
27893651751 = '278' + '93651751' is the concatenation of 2 semiprime numbers.

Number of the day: 1441685867545

Properties of the number 1441685867545:

1441685867545 = 5 × 7 × 11 × 19 × 43 × 613 × 7477 is composite and squarefree.
1441685867545 has 7 distinct prime factors, 128 divisors, 135 antidivisors and 830144609280 totatives.
Reversing the decimal digits of 1441685867545 results in a sphenic number.
1441685867545 = 1684³ + 3017³ + 11212³ is the sum of 3 positive cubes in 1 way.
1441685867545 is the difference of 2 nonnegative squares in 64 ways.
1441685867545 is the difference of 2 positive pentagonal numbers in 59 ways.
1441685867545 = 135² + 746² + 1200702² is the sum of 3 positive squares.
1441685867545² = 531845016164² + 1339999634127² = 378523767545² + 1391106717000² = 885771113073² + 1137483044236² = 797748525728² + 1200856123929² = 82314853775² + 1439334014580² = 929452291768² + 1102078299399² = 681145687684² + 1270629250737² = 217461000295² + 1425190813200² = 1009676050383² + 1029083288156² = 607486357401² + 1307447309168² = 298479299580² + 1410449661775² = 949272149672² + 1085053236729² = 865011520527² + 1153348694036² is the sum of 2 positive squares in 13 ways.
1441685867545² is the sum of 3 positive squares.
1441685867545 is a proper divisor of 1291⁵³⁴⁰ - 1.
1441685867545 = '1441685867' + '545' is the concatenation of 2 semiprime numbers.
1441685867545 = '144168586' + '7545' is the concatenation of 2 sphenic numbers.

Number of the day: 47991

Properties of the number 47991:

47991 is a cyclic number.
47991 = 3 × 17 × 941 is a sphenic number and squarefree.
47991 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 30080 totatives.
47991 has a sphenic digit sum 30 in base 10.
47991 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 47991 results in a sphenic number.
47991 = 23996² - 23995² = 8000² - 7997² = 1420² - 1403² = 496² - 445² is the difference of 2 nonnegative squares in 4 ways.
47991 is the sum of 2 positive triangular numbers.
47991 is the difference of 2 positive pentagonal numbers in 2 ways.
47991 is not the sum of 3 positive squares.
47991² = 22584² + 42345² = 19425² + 43884² = 8316² + 47265² = 29580² + 37791² is the sum of 2 positive squares in 4 ways.
47991² is the sum of 3 positive squares.
47991 is a proper divisor of 577¹⁰ - 1.
47991 = '47' + '991' is the concatenation of 2 prime numbers.
47991 = '4' + '7991' is the concatenation of 2 semiprime numbers.
47991 is palindromic in (at least) the following bases: 42, -12, and -49.
47991 in base 16 = bb77 and consists of only the digits '7' and 'b'.
47991 in base 36 = 1113 and consists of only the digits '1' and '3'.
47991 in base 37 = Z22 and consists of only the digits '2' and 'Z'.
47991 in base 39 = VLL and consists of only the digits 'L' and 'V'.
47991 in base 42 = R8R and consists of only the digits '8' and 'R'.
47991 in base 48 = Kdd and consists of only the digits 'K' and 'd'.

The number 47991 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A043615: Numbers n such that base 6 representation has exactly 7 runs.
A131205: a(n) = a(n-1) + a(floor(n/2)) + a(ceiling(n/2)).
A152560: a(n) = A131205(A005578(n)).