112

Number
$112$ (one hundred and twelve) is:


 * $2^4 \times 7$


 * The $7$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$:
 * $112 = 1 + 7 + 11 + 16 + 21 + 26 + 31 = \dfrac {7 \left({5 \times 7 - 3}\right)} 2$


 * The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $8$ different ways


 * The $16$th Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $15$, $24$, $36$, $111$:
 * $112 = 56 \times 2 = 56 \times \left({1 \times 1 \times 2}\right)$


 * The $30$th positive integer which is not the sum of $1$ or more distinct squares:
 * $2$, $3$, $6$, $7$, $8$, $11$, $12$, $15$, $18$, $19$, $22$, $23$, $24$, $27$, $28$, $31$, $32$, $33$, $43$, $44$, $47$, $48$, $60$, $67$, $72$, $76$, $92$, $96$, $108$, $112$, $\ldots$


 * The $53$rd positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $95$, $96$, $100$, $101$, $102$, $107$ which cannot be expressed as the sum of distinct pentagonal numbers


 * The length of the side of the smallest perfect square dissection of an integer square


 * The side length of the smallest equilateral triangle with sides of integer length which contains a point which is an integer distance from each vertex

Also see

 * Smallest Perfect Square Dissection
 * Smallest Equilateral Triangle with Internal Point at Integer Distances from Vertices