# 32

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## Contents

## Number

$32$ (**thirty-two**) is:

- $2^5$

- In binary:
- $100 \, 000$

- The $2$nd fifth power after $1$:
- $32 = 2 \times 2 \times 2 \times 2 \times 2$

- The $5$th power of $2$ after $(1)$, $2$, $4$, $8$, $16$:
- $32 = 2^5$

- The $6$th almost perfect number after $1$, $2$, $4$, $8$, $16$:
- $\sigma \left({32}\right) = 63 = 2 \times 32 - 1$

- The $8$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $27$

- The $9$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $28$, $31$:
- $32 \to 3^2 + 2^2 = 9 + 4 = 13 \to 1^2 + 3^2 = 9 + 1 = 10 \to 1^2 + 0^2 = 1$

- The $13$th even number after $2$, $4$, $6$, $8$, $10$, $12$, $14$, $16$, $20$, $22$, $26$, $28$ which cannot be expressed as the sum of $2$ composite odd numbers.

- The $18$th after $1$, $2$, $4$, $5$, $6$, $8$, $9$, $12$, $13$, $15$, $16$, $17$, $20$, $24$, $25$, $27$, $28$ of the $24$ positive integers which cannot be expressed as the sum of distinct non-pythagorean primes.

- The $22$nd integer $n$ such that $2^n$ contains no zero in its decimal representation:
- $2^{32} = 4 \, 294 \, 967 \, 296$

- The $17$th positive integer which is not the sum of $1$ or more distinct squares:
- $2$, $3$, $6$, $7$, $8$, $11$, $12$, $15$, $18$, $19$, $22$, $23$, $24$, $27$, $28$, $31$, $32$, $\ldots$

- The $21$st positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $26$, $29$, $30$, $31$ which cannot be expressed as the sum of distinct pentagonal numbers.

- The $2$nd element of the $2$nd pair of integers $m$ whose values of $m \tau \left({m}\right)$ is equal:
- $24 \times \tau \left({24}\right) = 192 = 32 \times \tau \left({32}\right)$

- The $8$th integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:
- $3$, $4$, $6$, $7$, $12$, $14$, $30$, $32$

## Also see

*Previous ... Next*: Powerful Number

*Previous ... Next*: Positive Integers Not Expressible as Sum of Distinct Non-Pythagorean Primes*Previous ... Next*: Positive Even Integers not Expressible as Sum of 2 Composite Odd Numbers

*Previous ... Next*: Powers of 2 with no Zero in Decimal Representation*Previous ... Next*: Numbers not Sum of Distinct Squares*Previous ... Next*: Numbers not Expressible as Sum of Distinct Pentagonal Numbers*Previous ... Next*: Happy Number

## Historical Note

$32 \ ^\circ \mathrm F$ is the melting point of water on the Fahrenheit scale.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $32$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $32$