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# 116 (number)

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 Title: 116 (number) Author: World Heritage Encyclopedia Language: English Subject: Collection: Integers Publisher: World Heritage Encyclopedia Publication Date:

### 116 (number)

 ← 115 116 117 →
Cardinal one hundred sixteen
Ordinal 116th
(one hundred and sixteenth)
Factorization 22× 29
Divisors 1, 2, 4, 29, 58, 116
Roman numeral CXVI
Binary 11101002
Ternary 110223
Quaternary 13104
Quinary 4315
Senary 3126
Octal 1648
Duodecimal 9812
Vigesimal 5G20
Base 36 3836

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

## Contents

• In mathematics 1
• In other fields 2
• References 4

## In mathematics

116 is a noncototient, meaning that there is no solution to the equation mφ(m) = n, where φ stands for Euler's totient function.[1] 116! + 1 is 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]

## In other fields

One hundred sixteen is also:

## References

1. ^ "Sloane's A005278 : Noncototients: n such that x-phi(x)=n has no solution", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
2. ^ "Sloane's A002981 : Numbers n such that n! + 1 is prime", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
3. ^ "Sloane's A027376 : Number of ternary irreducible polynomials of degree n; dimensions of free Lie algebras", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
4. ^ "Sloane's A007052 : Number of order-consecutive partitions of n", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
5. ^ "Sloane's A008404 : Number of Costas arrays of order n, counting rotations and flips as distinct", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
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