### Properties of the number 4991:

4991 = 7 × 23 × 31 is a sphenic number and squarefree.4991 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 3960 totatives.

4991 has a prime digit sum 23 in base 10.

Reversing the decimal digits of 4991 results in a semiprime.

4991 = 2496

^{2}- 2495

^{2}= 360

^{2}- 353

^{2}= 120

^{2}- 97

^{2}= 96

^{2}- 65

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

4991 is the difference of 2 positive pentagonal numbers in 3 ways.

4991 is not the sum of 3 positive squares.

4991

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

4991 is a divisor of 1427

^{2}- 1.

4991 = '49' + '91' is the concatenation of 2 semiprime numbers.

4991 is palindromic in (at least) the following bases: 19, -28, and -43.

4991 in base 19 = dfd and consists of only the digits 'd' and 'f'.

### The number 4991 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A001845: Centered octahedral numbers (crystal ball sequence for cubic lattice).

A004006: C(n,1) + C(n,2) + C(n,3), or n*(n^2+5)/6.

A005008: n! - n^2.

A006972: Lucas-Carmichael numbers: squarefree composite numbers n such that p | n => p+1 | n+1.

A152942: Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) has height 4.

A195575: Numerators b(n) of Pythagorean approximations b(n)/a(n) to 2/5.

A199118: Number of partitions of n into terms of (1,3)-Ulam sequence, cf. A002859.

A216925: Lucas-Carmichael numbers with 3 prime factors.

A257752: Quasi-Carmichael numbers to exactly two bases.

A263799: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nonincreasing