### Properties of the number 5192:

5192 = 2^{3}× 11 × 59 is the 4500

^{th}composite number and is not squarefree.

5192 has 3 distinct prime factors, 16 divisors, 11 antidivisors and 2320 totatives.

5192 has an emirp digit sum 17 in base 10.

5192 has an oblong digit product 90 in base 10.

Reversing the decimal digits of 5192 results in a sphenic number.

5192 = 1299

^{2}- 1297

^{2}= 651

^{2}- 647

^{2}= 129

^{2}- 107

^{2}= 81

^{2}- 37

^{2}is the difference of 2 nonnegative squares in 4 ways.

5192 is the difference of 2 positive pentagonal numbers in 1 way.

5192 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.

5192 = (59 × (3 × 59-1))/2 is a pentagonal number.

5192 = 6

^{2}+ 16

^{2}+ 70

^{2}is the sum of 3 positive squares.

5192

^{2}is the sum of 3 positive squares.

5192 is a divisor of 353

^{2}- 1.

5192 = '51' + '92' is the concatenation of 2 pentagonal numbers.

5192 is palindromic in (at least) the following bases: 20, and 87.

5192 in base 20 = cjc and consists of only the digits 'c' and 'j'.

5192 in base 41 = 33Q and consists of only the digits '3' and 'Q'.

### The number 5192 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A033570: Pentagonal numbers with odd index: (2*n+1)*(3*n+1).

A035005: Number of possible queen moves on an n X n chessboard.

A035959: Number of partitions of n in which no parts are multiples of 5.

A057687: Trajectory of 29 under the `29x+1' map.

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).

A116995: Pentagonal numbers with prime indices.

A136117: Pentagonal numbers (A000326) which are the sum of 2 other positive pentagonal numbers.

A152728: a(n)+a(n+1)+a(n+2)=n^3.

A252053: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum not 1 3 6 or 8 and every diagonal and antidiagonal sum 1 3 6 or 8

A270299: Numbers which are representable as a sum of eleven but no fewer consecutive nonnegative integers.

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