# 115

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## Number

$115$ (one hundred and fifteen) is:

$5 \times 23$

The $1$st 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 $n$:
$\left({115, 116, 117, 118, 119}\right)$

The $5$th heptagonal pyramidal number after $1$, $8$, $26$, $60$:
$115 = 1 + 7 + 18 + 34 + 55 = \dfrac {5 \paren {5 + 1} \paren {5 \times 5 - 2} } 6$

The index (after $2$, $3$, $6$, $30$, $75$, $81$) of the $7$th Woodall prime:
$115 \times 2^{115} - 1$

The $8$th number after $1$, $3$, $22$, $66$, $70$, $81$, $94$ whose $\sigma$ value is square:
$\map \sigma {115} = 144 = 12^2$

The $17$th Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $15$, $24$, $36$, $111$, $112$:
$115 = 23 \times 5 = 23 \times \paren {1 \times 1 \times 5}$

The $25$th lucky number:
$1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $43$, $49$, $51$, $63$, $67$, $73$, $75$, $79$, $87$, $93$, $99$, $105$, $111$, $115$, $\ldots$

The $36$th semiprime:
$115 = 5 \times 23$