114 (number)

Template:Infobox number 114 (one hundred [and] fourteen) is the natural number following 113 and preceding 115.

In mathematics

114 is an abundant number, a sphenic number<ref>Template:Cite OEIS</ref> and a Harshad number.<ref>Template:Cite OEIS</ref> It is the sum of the first four hyperfactorials, including H(0). At 114, the Mertens function 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 a³ + b³ + c³, 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.)<ref>{{#invoke:citation/CS1|citation

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There is no answer to the equation φ(x) = 114, making 114 a nontotient.<ref>Template:Cite OEIS</ref>
114 appears in the Padovan sequence,<ref>Template:Cite OEIS</ref> preceded by the terms 49, 65, 86 (it is the sum of the first two of these).
114 is a repdigit in base 7 (222).