115

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:


 * 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:
 * $115 = 5 \times 23$


 * The $38$th odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime
 * $1$, $\ldots$, $37$, $41$, $43$, $45$, $47$, $49$, $53$, $55$, $59$, $61$, $67$, $69$, $73$, $77$, $83$, $89$, $97$, $101$, $103$, $115$, $\ldots$