114
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Number
$114$ (one hundred and fourteen) is:
- $2 \times 3 \times 19$
- The number of different ways to colour the faces of a cube with $3$ given colours, one colour per face.
- The $9$th sphenic number after $30$, $42$, $66$, $70$, $78$, $102$, $105$, $110$:
- $114 = 2 \times 3 \times 19$
- The smallest positive integer which can be expressed as the sum of $2$ odd primes in $10$ ways.
- The $14$th nontotient after $14$, $26$, $34$, $38$, $50$, $62$, $68$, $74$, $76$, $86$, $90$, $94$, $98$:
- $\nexists m \in \Z_{>0}: \map \phi m = 114$
- where $\map \phi m$ denotes the Euler $\phi$ function
- The $54$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $77$, $78$, $79$, $84$, $90$, $91$, $95$, $96$, $102$, $108$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$
Also see
- Previous ... Next: Smallest Positive Integer which is Sum of 2 Odd Primes in n Ways
- Previous ... Next: Nontotient
- Previous ... Next: Integers not Expressible as Sum of Distinct Primes of form 6n-1
- Previous ... Next: Sphenic Number
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $114$