Number of the day: 51453

Properties of the number 51453:

51453 = 3² × 5717 is the 46187^th 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.

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

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.

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

Number of the day: 92424

Properties of the number 92424:

92424 = 2³ × 3 × 3851 is the 83494^th 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.

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.

Number of the day: 1352637

Properties of the number 1352637:

1352637 = 3² × 11 × 13 × 1051 is the 1248900^th 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.