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 $30$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