116 (one hundred
ndsixteen) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''Cardinal n ...
following
115 and preceding
117.
In mathematics
116 is a
noncototient In mathematics, a noncototient is a positive integer ''n'' that cannot be expressed as the difference between a positive integer ''m'' and the number of coprime integers below it. That is, ''m'' − φ(''m'') = ''n'', where Ï ...
, meaning that there is no solution to the equation , where stands for
Euler's totient function
In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In ot ...
.
116! + 1 is a
factorial prime
A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even).
The first 10 factorial primes (for ''n'' = 1, 2, 3, 4, 6, 7, 11, 12, 14) are :
: 2 (0! +&n ...
.
There are 116 ternary
Lyndon word
In mathematics, in the areas of combinatorics and computer science, a Lyndon word is a nonempty string that is strictly smaller in lexicographic order than all of its rotations. Lyndon words are named after mathematician Roger Lyndon, who investi ...
s of length six, and 116
irreducible polynomial
In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of irreducibility depends on the nature of the coefficients that are accepted ...
s of degree six over a three-element field, which form the basis of a
free Lie algebra In mathematics, a free Lie algebra over a field ''K'' is a Lie algebra generated by a set ''X'', without any imposed relations other than the defining relations of alternating ''K''-bilinearity and the Jacobi identity.
Definition
The definition ...
of dimension 116.
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.
There are 116 different 6×6
Costas array
In mathematics, a Costas array can be regarded geometrically as a set of ''n'' points, each at the center of a square in an ''n''×''n'' square tiling such that each row or column contains only one point, and all of the ''n''(''n'' &minu ...
s.
[.]
See also
*
116 (disambiguation) 116 (''one hundred and sixteen'') may refer to:
*116 (number)
*AD 116
*116 BC
*116 (Devon and Cornwall) Engineer Regiment, Royal Engineers, a military unit
*116 (MBTA bus)
*116 (New Jersey bus)
*116 (hip hop group), a Christian hip hop collective
* ...
References
{{DEFAULTSORT:116 (Number)
Integers