116

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Number

$116$ (one hundred and sixteen) is:

$2^2 \times 29$

The $2$nd term of the $2$nd $5$-tuple of consecutive integers have the property that they are not values of the divisor sum function $\map {\sigma_1} n$ 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:

$\map {\sigma_0} {116} = \map {\sigma_0} {117} = 6$

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 $11$th integer $m$ such that $m! + 1$ (its factorial plus $1$) is prime:

$0$, $1$, $2$, $3$, $11$, $27$, $37$, $41$, $73$, $77$, $116$

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.

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 Divisor Sum Values

Sources

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