# 116 (number)

From HandWiki

__: Natural number__

**Short description**
| ||||
---|---|---|---|---|

Cardinal | one hundred sixteen | |||

Ordinal | 116th (one hundred sixteenth) | |||

Factorization | 2^{2} × 29 | |||

Divisors | 1, 2, 4, 29, 58, 116 | |||

Greek numeral | ΡΙϚ´ | |||

Roman numeral | CXVI | |||

Binary | 1110100_{2} | |||

Ternary | 11022_{3} | |||

Quaternary | 1310_{4} | |||

Quinary | 431_{5} | |||

Senary | 312_{6} | |||

Octal | 164_{8} | |||

Duodecimal | 98_{12} | |||

Hexadecimal | 74_{16} | |||

Vigesimal | 5G_{20} | |||

Base 36 | 38_{36} |

**116** (**one hundred [and] sixteen**) is the natural number following 115 and preceding 117.

## 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

- 116 (disambiguation)

## References

- ↑ Sloane, N. J. A., ed. "Sequence A005278 (Noncototients: n such that x-phi(x)=n has no solution)". OEIS Foundation. https://oeis.org/A005278..
- ↑ Sloane, N. J. A., ed. "Sequence A002981 (Numbers n such that n! + 1 is prime)". OEIS Foundation. https://oeis.org/A002981..
- ↑ Sloane, N. J. A., ed. "Sequence A027376 (Number of ternary irreducible polynomials of degree n; dimensions of free Lie algebras)". OEIS Foundation. https://oeis.org/A027376..
- ↑ Sloane, N. J. A., ed. "Sequence A007052 (Number of order-consecutive partitions of n)". OEIS Foundation. https://oeis.org/A007052..
- ↑ Sloane, N. J. A., ed. "Sequence A008404 (Number of Costas arrays of order n, counting rotations and flips as distinct)". OEIS Foundation. https://oeis.org/A008404..

Original source: https://en.wikipedia.org/wiki/116 (number).
Read more |