Wikipedia
116 (number)
116 (one hundred [and] sixteen) is the natural number following 115 and preceding 117.
| Cardinal | one hundred sixteen |
|---|---|
| Ordinal | 116th (one hundred sixteenth) |
| Factorization | 22 × 29 |
| Divisors | 1, 2, 4, 29, 58, 116 |
| Greek numeral | ΡΙϚ´ |
| Roman numeral | CXVI |
| Binary | 11101002 |
| Ternary | 110223 |
| Senary | 3126 |
| Octal | 1648 |
| Duodecimal | 9812 |
| Hexadecimal | 7416 |
In mathematics
116 is a noncototient, meaning that there is no solution to the equation m − φ(m) = n, where φ stands for Euler's totient function.[1]
116! + 1 is a factorial prime.[2]
There are 116 ternary Lyndon words of length six, and 116 irreducible polynomials of degree six over a three-element field, which form the basis of a free Lie algebra of dimension 116.[3]
There are 116 different ways of partitioning the numbers from 1 through 5 into subsets in such a way that, for every k, the union of the first k subsets is a consecutive sequence of integers.[4]
There are 116 different 6×6 Costas arrays.[5]
See also
References
- ^ Sloane, N. J. A. (ed.). "Sequence A005278 (Noncototients: n such that x-phi(x)=n has no solution)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
- ^ Sloane, N. J. A. (ed.). "Sequence A002981 (Numbers n such that n! + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
- ^ Sloane, N. J. A. (ed.). "Sequence A027376 (Number of ternary irreducible polynomials of degree n; dimensions of free Lie algebras)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
- ^ Sloane, N. J. A. (ed.). "Sequence A007052 (Number of order-consecutive partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
- ^ Sloane, N. J. A. (ed.). "Sequence A008404 (Number of Costas arrays of order n, counting rotations and flips as distinct)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..