Wednesday, May 31, 2017

Number of the day: 51453

Properties of the number 51453:

51453 = 32 × 5717 is the 46187th composite number and is not squarefree.
51453 has 2 distinct prime factors, 6 divisors, 17 antidivisors and 34296 totatives.
51453 has a triangular digit product 300 in base 10.
51453 = 43 + 293 + 303 is the sum of 3 positive cubes in 1 way.
51453 = 257272 - 257262 = 85772 - 85742 = 28632 - 28542 is the difference of 2 nonnegative squares in 3 ways.
51453 is the difference of 2 positive pentagonal numbers in 1 way.
51453 = 782 + 2132 is the sum of 2 positive squares in 1 way.
51453 = 112 + 342 + 2242 is the sum of 3 positive squares.
514532 = 332282 + 392852 is the sum of 2 positive squares in 1 way.
514532 is the sum of 3 positive squares.
51453 is a proper divisor of 191429 - 1.
51453 = '5' + '1453' is the concatenation of 2 prime numbers.
51453 = '51' + '453' is the concatenation of 2 semiprime numbers.
51453 is palindromic in (at least) base -46.
51453 in base 7 = 303003 and consists of only the digits '0' and '3'.
51453 in base 45 = PII and consists of only the digits 'I' and 'P'.
51453 in base 49 = LL3 and consists of only the digits '3' and 'L'.

The number 51453 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033896: Sort then Add!.
A033903: Sort then Add!.
A272051: Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 421", based on the 5-celled von Neumann neighborhood.

Tuesday, May 30, 2017

Number of the day: 4682

Properties of the number 4682:

4682 = 2 × 2341 is semiprime and squarefree.
4682 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 2340 totatives.
4682 has an oblong digit sum 20 in base 10.
4682 has sum of divisors equal to 7026 which is a sphenic number.
4682 is the sum of 2 positive triangular numbers.
4682 = 312 + 612 is the sum of 2 positive squares in 1 way.
4682 = 72 + 122 + 672 is the sum of 3 positive squares.
46822 = 27602 + 37822 is the sum of 2 positive squares in 1 way.
46822 is the sum of 3 positive squares.
4682 is a proper divisor of 8095 - 1.
4682 = '46' + '82' is the concatenation of 2 semiprime numbers.
4682 is an emirpimes in (at least) the following bases: 5, 6, 8, 14, 19, 26, 28, 29, 30, 35, 36, 50, 53, 54, 56, 57, 58, 62, 63, 64, 68, 69, 70, 71, 72, 73, 75, 77, 79, 80, 82, 83, 84, 92, 95, 98, and 99.
4682 is palindromic in (at least) the following bases: 25, 40, 45, -8, -28, -52, -60, and -65.
4682 in base 5 = 122212 and consists of only the digits '1' and '2'.
4682 in base 8 = 11112 and consists of only the digits '1' and '2'.
4682 in base 25 = 7c7 and consists of only the digits '7' and 'c'.
4682 in base 27 = 6bb and consists of only the digits '6' and 'b'.
4682 in base 39 = 332 and consists of only the digits '2' and '3'.
4682 in base 40 = 2b2 and consists of only the digits '2' and 'b'.
4682 in base 44 = 2II and consists of only the digits '2' and 'I'.
4682 in base 45 = 2E2 and consists of only the digits '2' and 'E'.

The number 4682 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002219: a(n) is the number of partitions of 2n that can be obtained by adding together two (not necessarily distinct) partitions of n.
A046630: Number of cubic residues mod 2^n.
A047853: a(n)=T(5,n), array T given by A047848.
A052875: E.g.f.: (exp(x)-1)^2/(2-exp(x)).
A121350: Number of conjugacy class of index n subgroups in PSL_2 (ZZ).
A199120: Number of partitions of n into terms of (1,4)-Ulam sequence, cf. A003666.
A213375: Irregular array T(n,k) of numbers/2 of non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 5, n >= 2.
A213379: Irregular array T(n,k) of numbers/2 of non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 6, n >= 2.
A232376: T(n,k)=Number of nXk 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal
A252384: T(n,k)=Number of (n+2)X(k+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

Monday, May 29, 2017

Number of the day: 156554

Properties of the number 156554:

156554 = 2 × 78277 is semiprime and squarefree.
156554 has 2 distinct prime factors, 4 divisors, 3 antidivisors and 78276 totatives.
156554 has an emirpimes digit sum 26 in base 10.
156554 has sum of divisors equal to 234834 which is a sphenic number.
156554 = 232 + 3952 is the sum of 2 positive squares in 1 way.
156554 = 372 + 482 + 3912 is the sum of 3 positive squares.
1565542 = 181702 + 1554962 is the sum of 2 positive squares in 1 way.
1565542 is the sum of 3 positive squares.
156554 is a proper divisor of 92944 - 1.
156554 is an emirpimes in (at least) the following bases: 5, 7, 9, 12, 16, 24, 29, 30, 36, 38, 39, 43, 45, 47, 50, 53, 54, 56, 61, 62, 64, 65, 66, 68, 71, 73, 76, 78, 79, 81, 82, 84, 85, 86, 92, 94, 95, and 100.

The number 156554 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A031622: Numbers n such that continued fraction for sqrt(n) has odd period and central terms 34.

Sunday, May 28, 2017

Number of the day: 7334

Properties of the number 7334:

7334 = 2 × 19 × 193 is a sphenic number and squarefree.
7334 has 3 distinct prime factors, 8 divisors, 5 antidivisors and 3456 totatives.
7334 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 7334 results in a prime.
7334 = 32 + 102 + 852 is the sum of 3 positive squares.
73342 = 36102 + 63842 is the sum of 2 positive squares in 1 way.
73342 is the sum of 3 positive squares.
7334 is a proper divisor of 2773 - 1.
7334 is palindromic in (at least) the following bases: 52, and -78.
7334 in base 28 = 99q and consists of only the digits '9' and 'q'.
7334 in base 51 = 2ff and consists of only the digits '2' and 'f'.
7334 in base 52 = 2b2 and consists of only the digits '2' and 'b'.
7334 in base 60 = 22E and consists of only the digits '2' and 'E'.

The number 7334 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A026135: Number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also sum of numbers in row n+1 of the array T defined in A026120.
A051743: a(n) = (1/24)*n*(n + 5)*(n^2 + n + 6).
A105210: a(1) = 393; for n>1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).
A108433: Triangle read by rows: T(n,k) is number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1) and have k hills of the form ud (a hill is either a ud or a Udd starting at the x-axis).
A126264: a(n) = 5*n^2 + 3*n.
A172139: Number of ways to place 4 nonattacking zebras on an n X n board.
A191653: Number of n-step two-sided prudent self-avoiding walks ending at the north-west corner of their box.
A238335: Square roots of numbers in A238334.
A242606: Start of a triplet of consecutive squarefree numbers each of which has exactly 3 distinct prime factors.
A258522: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock sum of the two sums of the diagonal and antidiagonal minus the two sums of the central column and central row nondecreasing horizontally and vertically

Saturday, May 27, 2017

Number of the day: 92424

Properties of the number 92424:

92424 = 23 × 3 × 3851 is the 83494th composite number and is not squarefree.
92424 has 3 distinct prime factors, 16 divisors, 11 antidivisors and 30800 totatives.
92424 has a semiprime digit sum 21 in base 10.
92424 has a Fibonacci digit sum 21 in base 10.
92424 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 92424 results in a semiprime.
92424 = 231072 - 231052 = 115552 - 115512 = 77052 - 76992 = 38572 - 38452 is the difference of 2 nonnegative squares in 4 ways.
92424 is the difference of 2 positive pentagonal numbers in 2 ways.
92424 = 402 + 822 + 2902 is the sum of 3 positive squares.
924242 is the sum of 3 positive squares.
92424 is a proper divisor of 5310 - 1.
92424 = '9242' + '4' is the concatenation of 2 semiprime numbers.
92424 is palindromic in (at least) base -98.
92424 in base 55 = UUO and consists of only the digits 'O' and 'U'.
92424 in base 58 = RRU and consists of only the digits 'R' and 'U'.

The number 92424 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A031754: Least term in period of continued fraction for sqrt(n) is 76.

Friday, May 26, 2017

Number of the day: 821573296864

Properties of the number 821573296864:

821573296864 = 25 × 172 × 47 × 109 × 17341 is composite and not squarefree.
821573296864 has 5 distinct prime factors, 144 divisors, 43 antidivisors and 374903562240 totatives.
821573296864 has a prime digit sum 61 in base 10.
821573296864 is the difference of 2 nonnegative squares in 48 ways.
821573296864 is the difference of 2 positive pentagonal numbers in 11 ways.
821573296864 = 146282 + 155122 + 9061562 is the sum of 3 positive squares.
8215732968642 = 5034638496002 + 6492355768642 = 4576930823362 + 6822754022402 = 2195921080642 + 7916830099202 = 5400699763202 + 6191180039362 = 3176649235202 + 7576751800642 = 629456486402 + 8191584263362 = 2648862983362 + 7777004121602 = 65462968642 + 8215472160002 = 2524596216642 + 7818227558402 = 5615538703362 + 5996998689602 = 3923865988802 + 7218139920642 = 1451581012802 + 8086481359362 = 5663144529602 + 5952063696642 = 3866227279362 + 7249176148802 = 1387101840642 + 8097790852802 = 3299460400642 + 7524083284802 = 762604463362 + 8180262993602 = 1851826831362 + 8004311688002 = 5086209768642 + 6452033664002 = 4522421817602 + 6859006423362 = 2132770060802 + 7934075880642 = 2586811718402 + 7797863383362 is the sum of 2 positive squares in 22 ways.
8215732968642 is the sum of 3 positive squares.
821573296864 is a proper divisor of 11233128 - 1.

Thursday, May 25, 2017

Number of the day: 1352637

Properties of the number 1352637:

1352637 = 32 × 11 × 13 × 1051 is the 1248900th composite number and is not squarefree.
1352637 has 4 distinct prime factors, 24 divisors, 29 antidivisors and 756000 totatives.
1352637 = 1333 - 1003 is the difference of 2 positive cubes in 1 way.
1352637 is the difference of 2 nonnegative squares in 12 ways.
1352637 is the sum of 2 positive triangular numbers.
1352637 is the difference of 2 positive pentagonal numbers in 3 ways.
1352637 = 322 + 372 + 11622 is the sum of 3 positive squares.
13526372 = 5202452 + 12485882 is the sum of 2 positive squares in 1 way.
13526372 is the sum of 3 positive squares.
1352637 is a proper divisor of 12316 - 1.
1352637 in base 38 = OORR and consists of only the digits 'O' and 'R'.

The number 1352637 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A063017: Product of Catalan(n) and (3^n- 2^n +1)/2.

Tuesday, May 23, 2017

Number of the day: 8207

Edward Norton Lorenz was born on this day 100 years ago.

Properties of the number 8207:

8207 is a cyclic number.
8207 = 29 × 283 is semiprime and squarefree.
8207 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 7896 totatives.
8207 has an emirp digit sum 17 in base 10.
8207 = 41042 - 41032 = 1562 - 1272 is the difference of 2 nonnegative squares in 2 ways.
8207 is the difference of 2 positive pentagonal numbers in 2 ways.
8207 is not the sum of 3 positive squares.
82072 = 56602 + 59432 is the sum of 2 positive squares in 1 way.
82072 is the sum of 3 positive squares.
8207 is a proper divisor of 16994 - 1.
8207 is an emirpimes in (at least) the following bases: 4, 8, 9, 15, 17, 20, 23, 24, 26, 27, 35, 39, 40, 41, 46, 49, 50, 52, 60, 65, 69, 70, 71, 72, 73, 75, 76, 78, 80, 85, 86, 87, 92, 93, 94, and 95.
8207 in base 40 = 557 and consists of only the digits '5' and '7'.

The number 8207 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A052968: a(n) = 1 + 2^(n-1) + n for n > 0, a(0) = 2.
A066699: Numbers n such that binomial(2n,n)+1 is prime.
A074345: a(1) = 9; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A081691: From P-positions in a certain game.
A160379: Number of ON cells at n-th stage of three-dimensional version of the cellular automaton A160117 using cubes.
A164887: a(n) = smallest number that leads to a new fixed point under the base-2 Kaprekar map of A164884
A165778: Numbers n such that |2^n-57| is prime.
A190126: Numbers 1 through 10000 sorted lexicographically in binary representation.
A202849: Number of secondary structures of size n having no stacks of even length.
A251028: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements

Monday, May 22, 2017

Number of the day: 64154321115508

Properties of the number 64154321115508:

64154321115508 = 22 × 13 × 811 × 3083 × 493433 is composite and not squarefree.
64154321115508 has 5 distinct prime factors, 48 divisors, 51 antidivisors and 29563524322560 totatives.
64154321115508 has a semiprime digit sum 46 in base 10.
64154321115508 = 160385802788782 - 160385802788762 = 12337369445422 - 12337369445162 = 197763020182 - 197763003962 = 52022672022 - 52022610362 = 15212644822 - 15212433962 = 4002142422 - 4001340842 = 329975022 - 320106362 = 89149422 - 39143162 is the difference of 2 nonnegative squares in 8 ways.
64154321115508 is the difference of 2 positive pentagonal numbers in 7 ways.
64154321115508 = 229062 + 316442 + 80095442 is the sum of 3 positive squares.
641543211155082 = 165205181099402 + 619907202665922 = 85928756933602 + 635762487499082 = 390922937424802 + 508681578961082 = 246747388905802 + 592193733373922 is the sum of 2 positive squares in 4 ways.
641543211155082 is the sum of 3 positive squares.
64154321115508 is a proper divisor of 31125688470 - 1.

Sunday, May 21, 2017

Number of the day: 4820

Properties of the number 4820:

4820 = 22 × 5 × 241 is the 4170th composite number and is not squarefree.
4820 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 1920 totatives.
4820 has a semiprime digit sum 14 in base 10.
4820 = 12062 - 12042 = 2462 - 2362 is the difference of 2 nonnegative squares in 2 ways.
4820 is the difference of 2 positive pentagonal numbers in 2 ways.
4820 = 462 + 522 = 142 + 682 is the sum of 2 positive squares in 2 ways.
4820 = 182 + 202 + 642 is the sum of 3 positive squares.
48202 = 24002 + 41802 = 5882 + 47842 = 19042 + 44282 = 28922 + 38562 is the sum of 2 positive squares in 4 ways.
48202 is the sum of 3 positive squares.
4820 is a proper divisor of 6594 - 1.
4820 is palindromic in (at least) the following bases: 18, 19, 61, -21, -29, -66, and -79.
4820 in base 18 = efe and consists of only the digits 'e' and 'f'.
4820 in base 19 = d6d and consists of only the digits '6' and 'd'.
4820 in base 24 = 88k and consists of only the digits '8' and 'k'.
4820 in base 28 = 644 and consists of only the digits '4' and '6'.
4820 in base 60 = 1KK and consists of only the digits '1' and 'K'.
4820 in base 61 = 1I1 and consists of only the digits '1' and 'I'.

The number 4820 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000899: Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details).
A005969: Sum of fourth powers of Fibonacci numbers.
A008608: Number of n X n upper triangular matrices A of nonnegative integers such that a_1i + a_2i + ... + a_{i-1,i} - a_ii - a_{i,i+1} - ... - a_in = -1.
A052447: Number of simple 2-edge-connected unlabeled n-node graphs.
A063867: Number of solutions to +- 1 +- 2 +- 3 +- ... +- n = 0 or +- 1.
A129991: Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+241)^2 = y^2.
A164770: Numbers n with property that average digit of n^2 is 2.
A235098: T(n,k)=Number of (n+1)X(k+1) 0..5 arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 4, with no adjacent elements equal (constant stress tilted 1X1 tilings)
A265058: Coordination sequence for (2,3,8) tiling of hyperbolic plane.
A266650: Expansion of Product_{k>=1} (1 + x^k - x^(3*k)) / (1 - x^k).

Saturday, May 20, 2017

Number of the day: 21067

Properties of the number 21067:

21067 is a cyclic number.
21067 is the 2370th prime.
21067 has 17 antidivisors and 21066 totatives.
21067 = 105342 - 105332 is the difference of 2 nonnegative squares in 1 way.
21067 is the sum of 2 positive triangular numbers.
21067 is the difference of 2 positive pentagonal numbers in 1 way.
21067 = 152 + 312 + 1412 is the sum of 3 positive squares.
210672 is the sum of 3 positive squares.
21067 is a proper divisor of 233511 - 1.
21067 is an emirp in (at least) the following bases: 5, 13, 21, 29, 37, 41, 51, 53, 55, 59, 61, 62, 65, 69, 71, 73, 82, 89, 93, and 95.
21067 is palindromic in (at least) the following bases: 52, 54, and -38.
21067 in base 17 = 44f4 and consists of only the digits '4' and 'f'.
21067 in base 37 = FEE and consists of only the digits 'E' and 'F'.
21067 in base 52 = 7f7 and consists of only the digits '7' and 'f'.
21067 in base 53 = 7QQ and consists of only the digits '7' and 'Q'.
21067 in base 54 = 7C7 and consists of only the digits '7' and 'C'.

The number 21067 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A023327: Numbers n such that n remains prime through 4 iterations of function f(x) = 9x + 10.
A023355: Numbers n such that n remains prime through 5 iterations of function f(x) = 9x + 10.
A046014: Discriminants of imaginary quadratic fields with class number 17 (negated).
A051334: Euclid-Mullin sequence (A000945) with initial value a(1)=8191 instead of a(1)=2.
A077345: a(n) is the n-th prime whose decimal expansion begins with the decimal expansion of n.
A142820: Primes congruent to 22 mod 61.
A174812: Primes of the form n^2+42.
A180452: Primes of the form floor(n^sqrt(pi)).
A261210: a(n) = gpf(1 + Product_{k=0..4} prime(n+k)), where gpf is greatest prime factor and prime(i) is the i-th prime.
A272421: Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 470", based on the 5-celled von Neumann neighborhood.

Friday, May 19, 2017

Number of the day: 73904

Properties of the number 73904:

73904 = 24 × 31 × 149 is the 66609th composite number and is not squarefree.
73904 has 3 distinct prime factors, 20 divisors, 15 antidivisors and 35520 totatives.
73904 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 73904 results in a sphenic number.
73904 = 332 + … + 632 is the sum of at least 2 consecutive positive squares in 1 way.
73904 = 184772 - 184752 = 92402 - 92362 = 46232 - 46152 = 6272 - 5652 = 3602 - 2362 = 2732 - 252 is the difference of 2 nonnegative squares in 6 ways.
73904 is the difference of 2 positive pentagonal numbers in 2 ways.
73904 = 522 + 602 + 2602 is the sum of 3 positive squares.
739042 = 252962 + 694402 is the sum of 2 positive squares in 1 way.
739042 is the sum of 3 positive squares.
73904 is a proper divisor of 14892 - 1.
73904 is palindromic in (at least) base 48.
73904 in base 48 = W3W and consists of only the digits '3' and 'W'.

Thursday, May 18, 2017

Number of the day: 701955

Bertrand Russell was born on this day 145 years ago.

Properties of the number 701955:

701955 = 32 × 5 × 19 × 821 is the 645268th composite number and is not squarefree.
701955 has 4 distinct prime factors, 24 divisors, 35 antidivisors and 354240 totatives.
701955 is the difference of 2 nonnegative squares in 12 ways.
701955 is the sum of 2 positive triangular numbers.
701955 is the difference of 2 positive pentagonal numbers in 3 ways.
701955 = 492 + 1252 + 8272 is the sum of 3 positive squares.
7019552 = 4211732 + 5615642 = 656642 + 6988772 = 2587232 + 6525362 = 3667952 + 5985002 is the sum of 2 positive squares in 4 ways.
7019552 is the sum of 3 positive squares.
701955 is a proper divisor of 68320 - 1.
701955 = '70' + '1955' is the concatenation of 2 sphenic numbers.

Wednesday, May 17, 2017

Number of the day: 5385

Properties of the number 5385:

5385 is a cyclic number.
5385 = 3 × 5 × 359 is a sphenic number and squarefree.
5385 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 2864 totatives.
5385 has a semiprime digit sum 21 in base 10.
5385 has a Fibonacci digit sum 21 in base 10.
5385 has a triangular digit sum 21 in base 10.
5385 has an oblong digit product 600 in base 10.
Reversing the decimal digits of 5385 results in a sphenic number.
5385 = 82 + … + 252 is the sum of at least 2 consecutive positive squares in 1 way.
5385 = (30 × 31)/2 + … + (38 × 39)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
5385 = 26932 - 26922 = 8992 - 8962 = 5412 - 5362 = 1872 - 1722 is the difference of 2 nonnegative squares in 4 ways.
5385 is the sum of 2 positive triangular numbers.
5385 is the difference of 2 positive pentagonal numbers in 2 ways.
5385 = 192 + 202 + 682 is the sum of 3 positive squares.
53852 = 32312 + 43082 is the sum of 2 positive squares in 1 way.
53852 is the sum of 3 positive squares.
5385 is a proper divisor of 7192 - 1.
5385 is palindromic in (at least) the following bases: 24, 39, and -46.
5385 in base 24 = 989 and consists of only the digits '8' and '9'.
5385 in base 38 = 3RR and consists of only the digits '3' and 'R'.
5385 in base 39 = 3L3 and consists of only the digits '3' and 'L'.

The number 5385 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A015617: Number of (unordered) triples of integers from [1,n] with no common factors between pairs.
A056219: Number of partitions of n in SPM(n): these are the partitions obtained from (n) by iteration of the following transformation: p -> p' if p' is a partition (i.e., decreasing) and p' is obtained from p by removing a unit from the i-th component of p and adding one to the (i+1)-th component, for any i.
A144698: Triangle of 4-Eulerian numbers.
A160353: Numbers of the form pqr, where p<q<r are odd primes such that r = +/-1 (mod pq).
A164578: Integers of the form (k+1)*(2k+1)/12.
A180839: T(n,k)=number of nXk arrays containing k indistinguishable copies of 1..n with rows and columns in lexicographically strictly increasing order
A187283: T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every 2X2 subblock sum equal to some diagonal or antidiagonal neighbor 2X2 subblock sum
A224690: T(n,k)=Number of (n+4)X(k+4) 0..1 matrices with each 5X5 subblock idempotent
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.
A273707: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 873", based on the 5-celled von Neumann neighborhood.

Tuesday, May 16, 2017

Number of the day: 261497

Pafnuty Lvovich Chebyshev was born on this day 196 years ago.

Properties of the number 261497:

261497 is a cyclic number.
261497 = 19 × 13763 is semiprime and squarefree.
261497 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 247716 totatives.
261497 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 261497 results in a sphenic number.
261497 = 1307492 - 1307482 = 68912 - 68722 is the difference of 2 nonnegative squares in 2 ways.
261497 is the difference of 2 positive pentagonal numbers in 2 ways.
261497 = 272 + 522 + 5082 is the sum of 3 positive squares.
2614972 is the sum of 3 positive squares.
261497 is a proper divisor of 157126 - 1.
261497 = '26' + '1497' is the concatenation of 2 emirpimes.
261497 is an emirpimes in (at least) the following bases: 2, 3, 4, 6, 7, 11, 17, 21, 22, 29, 30, 31, 32, 39, 41, 43, 49, 51, 57, 58, 60, 63, 71, 76, 79, 83, 84, 87, 90, 92, 93, 94, 95, 97, and 98.
261497 is palindromic in (at least) the following bases: -75, and -85.
261497 in base 44 = 3335 and consists of only the digits '3' and '5'.

Monday, May 15, 2017

Number of the day: 2384565

Properties of the number 2384565:

2384565 = 3 × 5 × 43 × 3697 is the 2209330th composite number and is squarefree.
2384565 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 1241856 totatives.
2384565 has a semiprime digit sum 33 in base 10.
2384565 = 11922832 - 11922822 = 3974292 - 3974262 = 2384592 - 2384542 = 794932 - 794782 = 277492 - 277062 = 93072 - 91782 = 56532 - 54382 = 21712 - 15262 is the difference of 2 nonnegative squares in 8 ways.
2384565 is the difference of 2 positive pentagonal numbers in 4 ways.
2384565 = 252 + 1362 + 15382 is the sum of 3 positive squares.
23845652 = 14307392 + 19076522 = 7951562 + 22480832 = 13928132 + 19355162 = 7127252 + 22755602 is the sum of 2 positive squares in 4 ways.
23845652 is the sum of 3 positive squares.
2384565 is a proper divisor of 64142 - 1.
2384565 = '238' + '4565' is the concatenation of 2 sphenic numbers.

Sunday, May 14, 2017

Number of the day: 839

Properties of the number 839:

839 is a cyclic number.
839 is the 146th prime.
839 has 9 antidivisors and 838 totatives.
839 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 839 results in a sphenic number.
839 = 4202 - 4192 is the difference of 2 nonnegative squares in 1 way.
839 is the sum of 2 positive triangular numbers.
839 is the difference of 2 positive pentagonal numbers in 1 way.
839 is not the sum of 3 positive squares.
8392 is the sum of 3 positive squares.
839 is a proper divisor of 2419 - 1.
839 is an emirp in (at least) the following bases: 2, 7, 11, 12, 21, 25, 26, 27, 29, 31, 33, 35, 36, 37, 42, 44, 49, 53, 57, 61, 64, 65, 67, 71, 74, 75, 76, 77, 79, 83, 85, 89, and 92.
839 is palindromic in (at least) the following bases: 4, -10, -19, and -27.
839 in base 28 = 11r and consists of only the digits '1' and 'r'.

The number 839 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000928: Irregular primes: p is regular if and only if the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) are not divisible by p.
A005385: Safe primes p: (p-1)/2 is also prime.
A007522: Primes of the form 8n+7, that is, primes congruent to -1 mod 8.
A008865: a(n) = n^2 - 2.
A014616: a(n) = solution to the postage stamp problem with 2 denominations and n stamps.
A028871: Primes of the form n^2 - 2.
A068231: Primes congruent to 11 mod 12.
A107132: Primes of the form 2x^2 + 13y^2.
A141123: Primes of the form -x^2+2*x*y+2*y^2 (as well as of the form 3*x^2+6*x*y+2*y^2).
A235229: Numbers whose sum of digits is 20.

Saturday, May 13, 2017

Number of the day: 3716

Properties of the number 3716:

3716 = 22 × 929 is the 3197th composite number and is not squarefree.
3716 has 2 distinct prime factors, 6 divisors, 3 antidivisors and 1856 totatives.
3716 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 3716 results in a prime.
3716 = 9302 - 9282 is the difference of 2 nonnegative squares in 1 way.
3716 is the difference of 2 positive pentagonal numbers in 1 way.
3716 = 402 + 462 is the sum of 2 positive squares in 1 way.
3716 = 42 + 102 + 602 is the sum of 3 positive squares.
37162 = 5162 + 36802 is the sum of 2 positive squares in 1 way.
37162 is the sum of 3 positive squares.
3716 is a divisor of 9118 - 1.
3716 = '371' + '6' is the concatenation of 2 semiprime numbers.
3716 is palindromic in (at least) the following bases: 29, -19, and -32.
3716 in base 18 = b88 and consists of only the digits '8' and 'b'.
3716 in base 21 = 88k and consists of only the digits '8' and 'k'.
3716 in base 28 = 4kk and consists of only the digits '4' and 'k'.
3716 in base 29 = 4c4 and consists of only the digits '4' and 'c'.
3716 in base 60 = 11u and consists of only the digits '1' and 'u'.

The number 3716 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007042: Diagonal of partition triangle A047812.
A081579: Pascal-(1,4,1) array.
A124560: Rectangular table, read by antidiagonals, such that the g.f. of row n, R_n(y), satisfies: R_n(y) = Sum_{k>=0} y^k * [R_{n*k}(y)]^(n*k) for n>=0, with R_0(y)=1/(1-y).
A124562: Row 2 of table A124560; also, the self-convolution square equals A124552, which is row 2 of table A124550.
A196138: 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 0,2,1,3,4 for x=0,1,2,3,4
A203355: T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 010 and 101 in rows, columns and nw-to-se diagonals
A204197: T(n,k)=Number of nXk 0..1 arrays with no occurence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..1 introduced in row major order
A213109: E.g.f.: A(x) = exp( x/A(-x*A(x)^3) ).
A230092: Numbers of the form k + wt(k) for exactly three distinct k, where wt(k) = A000120(k) is the binary weight of k.
A273357: Numbers n such that the decimal number concat(2,n) is a square.

Friday, May 12, 2017

Number of the day: 85318

Properties of the number 85318:

85318 = 2 × 29 × 1471 is a sphenic number and squarefree.
85318 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 41160 totatives.
85318 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 85318 results in a sphenic number.
85318 is the sum of 2 positive triangular numbers.
85318 is the difference of 2 positive pentagonal numbers in 2 ways.
85318 = 272 + 582 + 2852 is the sum of 3 positive squares.
853182 = 588402 + 617822 is the sum of 2 positive squares in 1 way.
853182 is the sum of 3 positive squares.
85318 is a divisor of 52310 - 1.
85318 is palindromic in (at least) base -45.

The number 85318 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A059038: Triangle in A059037 read by rows from left to right.
A059039: Triangle in A059037 read by rows in natural order.
A090453: Third column (m=4) of array A090452.
A229082: Number of circular permutations i_0, i_1, ..., i_n of 0, 1, ..., n such that all the n+1 numbers i_0^2+i_1, i_1^2+i_2, ..., i_{n-1}^2+i_n, i_n^2+i_0 are of the form (p-1)/2 with p an odd prime.

Thursday, May 11, 2017

Number of the day: 10360266907667

Properties of the number 10360266907667:

10360266907667 = 29 × 98899 × 3612277 is a sphenic number and squarefree.
10360266907667 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 10002912411744 totatives.
10360266907667 has a prime digit sum 59 in base 10.
Reversing the decimal digits of 10360266907667 results in a prime.
10360266907667 = 51801334538342 - 51801334538332 = 1786252915262 - 1786252914972 = 524274662 - 523285672 = 32401742 - 3721032 is the difference of 2 nonnegative squares in 4 ways.
10360266907667 is the difference of 2 positive pentagonal numbers in 3 ways.
10360266907667 = 24292 + 24512 + 32187352 is the sum of 3 positive squares.
103602669076672 = 71450116604602 + 75022622434832 = 42961028362052 + 94275463838082 = 38313876107922 + 96257778581252 = 38640143908922 + 96127271460852 is the sum of 2 positive squares in 4 ways.
103602669076672 is the sum of 3 positive squares.
10360266907667 is a divisor of 1913367537934 - 1.
10360266907667 = '10360266907' + '667' is the concatenation of 2 semiprime numbers.

Wednesday, May 10, 2017

Number of the day: 8211515

Properties of the number 8211515:

8211515 = 5 × 13 × 19 × 61 × 109 is the 7658459th composite number and is squarefree.
8211515 has 5 distinct prime factors, 32 divisors, 53 antidivisors and 5598720 totatives.
8211515 has a prime digit sum 23 in base 10.
8211515 is the difference of 2 nonnegative squares in 16 ways.
8211515 is the difference of 2 positive pentagonal numbers in 14 ways.
8211515 = 152 + 2212 + 28572 is the sum of 3 positive squares.
82115152 = 56822352 + 59280002 = 29651402 + 76574752 = 32865252 + 75251402 = 22223732 + 79050642 = 9889882 + 81517412 = 40481972 + 71443042 = 18858642 + 79920272 = 13330592 + 81025882 = 43468962 + 69665972 = 36615282 + 73499792 = 5529572 + 81928762 = 53763162 + 62067872 = 17396402 + 80251252 = 14807652 + 80769002 = 44733602 + 68860752 = 55730612 + 60307522 = 28248442 + 77103332 = 34233632 + 74638842 = 32097652 + 75582002 = 558602 + 82113252 = 57422752 + 58698602 = 19671082 + 79724192 = 12505232 + 81157362 = 48821072 + 66025762 = 41207012 + 71027322 = 10719042 + 81412532 = 49714832 + 65355442 = 45201002 + 68554852 = 15356752 + 80666402 = 45896402 + 68091252 = 26935162 + 77571872 = 4972112 + 81964482 = 36114442 + 73747172 = 27723282 + 77293712 = 4137632 + 82010842 = 55319072 + 60685242 = 49269092 + 65692122 = 20212962 + 79588532 = 41689232 + 70745362 = 31582752 + 75798602 is the sum of 2 positive squares in 40 ways.
82115152 is the sum of 3 positive squares.
8211515 is a divisor of 149312 - 1.

Tuesday, May 9, 2017

Number of the day: 13143443117929

Gaspard Monge was born on this day 271 years ago.

Properties of the number 13143443117929:

13143443117929 is prime.
13143443117929 has 21 antidivisors and 13143443117928 totatives.
Reversing the decimal digits of 13143443117929 results in a semiprime.
13143443117929 = 65717215589652 - 65717215589642 is the difference of 2 nonnegative squares in 1 way.
13143443117929 is the difference of 2 positive pentagonal numbers in 1 way.
13143443117929 = 10210052 + 34786482 is the sum of 2 positive squares in 1 way.
13143443117929 = 87032 + 194622 + 36253262 is the sum of 3 positive squares.
131434431179292 = 71034340024802 + 110585406978792 is the sum of 2 positive squares in 1 way.
131434431179292 is the sum of 3 positive squares.
13143443117929 is a divisor of 251547643463247 - 1.
13143443117929 is an emirp in (at least) the following bases: 12, 31, and 34.

Monday, May 8, 2017

Number of the day: 649723

Properties of the number 649723:

649723 = 17 × 38219 is semiprime and squarefree.
649723 has 2 distinct prime factors, 4 divisors, 21 antidivisors and 611488 totatives.
649723 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 649723 results in an emirpimes.
649723 = 3248622 - 3248612 = 191182 - 191012 is the difference of 2 nonnegative squares in 2 ways.
649723 is the difference of 2 positive pentagonal numbers in 2 ways.
649723 = 32 + 1332 + 7952 is the sum of 3 positive squares.
6497232 = 3057522 + 5732852 is the sum of 2 positive squares in 1 way.
6497232 is the sum of 3 positive squares.
649723 is a divisor of 859776 - 1.
649723 = '6' + '49723' is the concatenation of 2 semiprime numbers.
649723 is an emirpimes in (at least) the following bases: 3, 5, 7, 9, 10, 12, 13, 15, 17, 21, 23, 25, 28, 36, 37, 38, 44, 45, 49, 60, 70, 71, 73, 74, 76, 77, 83, 85, 88, 91, 94, and 98.

The number 649723 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A286232: Sum T(n,k) of the entries in the k-th last blocks of all set partitions of [n]; triangle T(n,k), n>=1, 1<=k<=n, read by rows.

Sunday, May 7, 2017

Number of the day: 4606

Properties of the number 4606:

4606 = 2 × 72 × 47 is the 3982th composite number and is not squarefree.
4606 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 1932 totatives.
4606 is the difference of 2 positive pentagonal numbers in 5 ways.
4606 = 62 + 332 + 592 is the sum of 3 positive squares.
46062 is the sum of 3 positive squares.
4606 is a divisor of 6597 - 1.
4606 is palindromic in (at least) the following bases: 93, 97, -17, and -39.
4606 in base 17 = ffg and consists of only the digits 'f' and 'g'.

The number 4606 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A054098: Triangular array generated by its row sums: T(n,0)=1 for n >= 0, T(1,1)=2, T(n,k)=T(n,k-1)+d*r(n-k) for k=2,3,...,n, d=(-1)^(k+1), n >= 2, r(h)=sum of the numbers in row h of T.
A061147: Product of all distinct numbers formed by permuting digits of n.
A061205: a(n) = n times R(n) where R(n) (A004086) is the digit reversal of n.
A068634: a(n) = LCM (n, R(n)), where R(n) (A004086) = digit reversal of n.
A083074: n^3 - n^2 - n - 1.
A127596: Numbers n such that 1 + Sum{k=1..n-1} A001223(k)*(-1)^k = 0.
A169678: The second of a pair of sequences A and B with property that all the differences |a_i - b_j| are distinct - for precise definition see Comments lines in A169677.
A185875: Third accumulation array of A051340, by antidiagonals.
A245577: Numbers n such that n^4 is a sum of 4 consecutive primes.
A283357: Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 621", based on the 5-celled von Neumann neighborhood.

Saturday, May 6, 2017

Number of the day: 9462718250

André Weil was born on this day 111 years ago.

Properties of the number 9462718250:

9462718250 = 2 × 53 × 37850873 is the 9031028754th composite number and is not squarefree.
9462718250 has 3 distinct prime factors, 16 divisors, 13 antidivisors and 3785087200 totatives.
9462718250 is the difference of 2 positive pentagonal numbers in 4 ways.
9462718250 = 540852 + 808552 = 52452 + 971352 = 322332 + 917812 = 624772 + 745612 is the sum of 2 positive squares in 4 ways.
9462718250 = 4572 + 21802 + 972512 is the sum of 3 positive squares.
94627182502 = 48294620002 + 81375262502 = 10189461502 + 94076982002 = 36123438002 + 87460853502 = 64597758402 + 69147908702 = 23577761702 + 91642745602 = 16559671922 + 93166951942 = 59167539462 + 73847856722 = 56776309502 + 75701746002 = 26495611102 + 90842095202 = 33308768242 + 88571042822 is the sum of 2 positive squares in 10 ways.
94627182502 is the sum of 3 positive squares.
9462718250 is a divisor of 557461596 - 1.

Friday, May 5, 2017

Number of the day: 344649

Properties of the number 344649:

344649 = 3 × 114883 is semiprime and squarefree.
344649 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 229764 totatives.
344649 has a sphenic digit sum 30 in base 10.
344649 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 344649 results in an emirpimes.
344649 = 1723252 - 1723242 = 574432 - 574402 is the difference of 2 nonnegative squares in 2 ways.
344649 is the difference of 2 positive pentagonal numbers in 1 way.
344649 = 282 + 532 + 5842 is the sum of 3 positive squares.
3446492 is the sum of 3 positive squares.
344649 is a divisor of 82341 - 1.
344649 = '3446' + '49' is the concatenation of 2 emirpimes.
344649 is an emirpimes in (at least) the following bases: 7, 9, 10, 15, 27, 35, 43, 57, 58, 63, 64, 76, 80, 81, 85, 93, and 99.
344649 is palindromic in (at least) base -86.

Thursday, May 4, 2017

Number of the day: 775582

Properties of the number 775582:

775582 = 2 × 387791 is semiprime and squarefree.
775582 has 2 distinct prime factors, 4 divisors, 63 antidivisors and 387790 totatives.
775582 has a semiprime digit sum 34 in base 10.
775582 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 775582 results in an emirpimes.
775582 is the difference of 2 positive pentagonal numbers in 2 ways.
775582 = 222 + 1532 + 8672 is the sum of 3 positive squares.
7755822 is the sum of 3 positive squares.
775582 is a divisor of 611235 - 1.
775582 = '77' + '5582' is the concatenation of 2 semiprime numbers.
775582 is an emirpimes in (at least) the following bases: 3, 5, 7, 10, 12, 13, 14, 23, 24, 26, 34, 37, 48, 52, 58, 61, 62, 72, 76, 77, 78, 79, 80, 85, 88, 90, 92, and 94.

Wednesday, May 3, 2017

Number of the day: 915633127196684

Properties of the number 915633127196684:

915633127196684 = 22 × 13 × 1979 × 24061 × 369793 is composite and not squarefree.
915633127196684 has 5 distinct prime factors, 48 divisors, 79 antidivisors and 422367665725440 totatives.
915633127196684 has an emirp digit sum 71 in base 10.
915633127196684 = 2289082817991722 - 2289082817991702 = 176083293691802 - 176083293691542 = 1156686638282 - 1156686598702 = 95136885722 - 95136404502 = 88976151002 - 88975636462 = 7321331402 - 7315075542 = 6193871402 - 6186475542 = 524240282 - 428094102 is the difference of 2 nonnegative squares in 8 ways.
915633127196684 is the difference of 2 positive pentagonal numbers in 7 ways.
915633127196684 = 523382 + 556222 + 302593342 is the sum of 3 positive squares.
9156331271966842 = 6036455315960162 + 6884737437289402 = 5486177421603842 + 7330774833582202 = 4903065914816162 + 7732939091766202 = 2924136661928842 + 8676855832867202 = 2244634991641162 + 8876937316231202 = 1551699655304842 + 9023892205790402 = 5252303040547202 + 7500114341278842 = 4656800838074402 + 7883692555935162 = 4033428666744002 + 8220088536766842 = 4164496866638202 + 8154469216923842 = 3521665873833402 + 8451998097200162 = 2857758455035002 + 8698943555091842 = 707816639618402 + 9128931918175162 is the sum of 2 positive squares in 13 ways.
9156331271966842 is the sum of 3 positive squares.
915633127196684 is a divisor of 421473693280 - 1.

Tuesday, May 2, 2017

Number of the day: 52304

Properties of the number 52304:

52304 = 24 × 7 × 467 is the 46956th composite number and is not squarefree.
52304 has 3 distinct prime factors, 20 divisors, 15 antidivisors and 22368 totatives.
52304 has a semiprime digit sum 14 in base 10.
52304 = 130772 - 130752 = 65402 - 65362 = 32732 - 32652 = 18752 - 18612 = 9482 - 9202 = 4952 - 4392 is the difference of 2 nonnegative squares in 6 ways.
52304 is the difference of 2 positive pentagonal numbers in 1 way.
52304 = 322 + 682 + 2162 is the sum of 3 positive squares.
523042 is the sum of 3 positive squares.
52304 is a divisor of 186712 - 1.
52304 is palindromic in (at least) the following bases: 49, -63, and -68.
52304 in base 49 = LcL and consists of only the digits 'L' and 'c'.

Monday, May 1, 2017

Number of the day: 701220

Properties of the number 701220:

701220 = 22 × 3 × 5 × 13 × 29 × 31 is the 644588th composite number and is not squarefree.
701220 has 6 distinct prime factors, 96 divisors, 33 antidivisors and 161280 totatives.
701220 has an oblong digit sum 12 in base 10.
701220 is the difference of 2 nonnegative squares in 16 ways.
701220 is the difference of 2 positive pentagonal numbers in 5 ways.
701220 = 22 + 2602 + 7962 is the sum of 3 positive squares.
7012202 = 4207322 + 5609762 = 1160642 + 6915482 = 822122 + 6963842 = 3731162 + 5937122 = 1726082 + 6796442 = 3437282 + 6111962 = 3560042 + 6041282 = 1919522 + 6744362 = 1588442 + 6829922 = 2827202 + 6417002 = 2697002 + 6472802 = 2511002 + 6547202 = 4836002 + 5077802 is the sum of 2 positive squares in 13 ways.
7012202 is the sum of 3 positive squares.
701220 is a divisor of 5216 - 1.

The number 701220 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A171259: Numbers n such that sigma(n) = 14*phi(n) (where sigma=A000203, phi=A000010).
A249065: Numbers n such that n = concatenate(a, b) and sigma(a) + sigma(b) = phi(n).