114 (one hundred
ndfourteen) 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 ...
following
113 and preceding
115 115 may refer to:
* 115 (number), the number
* AD 115, a year in the 2nd century AD
* 115 BC, a year in the 2nd century BC
* 115 (Hampshire Fortress) Corps Engineer Regiment, Royal Engineers, a unit in the UK Territorial Army
* 115 (Leicestershire) ...
.
In mathematics
*114 is an
abundant number
In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. Th ...
, a
sphenic number
In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definit ...
and a
Harshad number. It is the sum of the first four
hyperfactorial
In mathematics, and more specifically number theory, the hyperfactorial of a positive integer n is the product of the numbers of the form x^x from 1^1 to n^n.
Definition
The hyperfactorial of a positive integer n is the product of the numbers ...
s, including H(0). At 114, the
Mertens function
In number theory, the Mertens function is defined for all positive integers ''n'' as
: M(n) = \sum_^n \mu(k),
where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive re ...
sets a new low of -6, a record that stands until 197.
*114 is the smallest positive integer* which has yet to be represented as a
3 + b
3 + c
3,
where a, b, and c are integers. It is conjectured that 114 can be represented this way. (*Excluding integers of the form 9k ± 4, for which solutions are known not to exist.)
*There is no answer to the equation
φ(x) = 114, making 114 a
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...
.
*114 appears in the
Padovan sequence,
preceded by the terms 49, 65, 86 (it is the sum of the first two of these).
*114 is a
repdigit
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit.
Example ...
in base 7 (222).
See also
*
114 (disambiguation)
References
{{DEFAULTSORT:114 (Number)
Integers