112
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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
Historical Note
$112$ is the number of pounds avoirdupois in a hundredweight.
Also see
- Smallest Perfect Square Dissection
- Smallest Equilateral Triangle with Internal Point at Integer Distances from Vertices
- Previous ... Next: Smallest Sum of 2 Lucky Numbers in n Ways
- Previous ... Next: Heptagonal Number
- Previous ... Next: Numbers not Expressible as Sum of Distinct Pentagonal Numbers
- Previous ... Next: Numbers not Sum of Distinct Squares
- Previous ... Next: Zuckerman Number
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $112$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $112$