# 116

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## Number

$116$ (**one hundred and sixteen**) is:

- $2^2 \times 29$

- The $9$th noncototient after $10$, $26$, $34$, $50$, $52$, $58$, $86$, $100$:
- $\nexists m \in \Z_{>0}: m - \map \phi m = 116$

- where $\map \phi m$ denotes the Euler $\phi$ function

- The $2$nd term of the $2$nd $5$-tuple of consecutive integers have the property that they are not values of the $\sigma$ function $\map \sigma n$ for any $n$:
- $\tuple {115, 116, 117, 118, 119}$

- The $1$st of the $4$th pair of consecutive integers which both have $6$ divisors:
- $\map \tau {116} = \map \tau {117} = 6$

- The $22$nd positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.

- The $54$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $95$, $96$, $100$, $101$, $102$, $107$, $112$ which cannot be expressed as the sum of distinct pentagonal numbers.

- The $11$th integer $m$ such that $m! + 1$ (its factorial plus $1$) is prime:
- $0$, $1$, $2$, $3$, $11$, $27$, $37$, $41$, $73$, $77$, $116$

## Also see

*Previous ... Next*: Sequence of Integers whose Factorial plus 1 is Prime*Previous ... Next*: Pairs of Consecutive Integers with 6 Divisors*Previous ... Next*: Noncototient*Previous ... Next*: Numbers of Zeroes that Factorial does not end with*Previous ... Next*: Numbers not Expressible as Sum of Distinct Pentagonal Numbers*Previous ... Next*: Quintuplets of Consecutive Integers which are not Sigma Values

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $116$