32

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 $6$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:
 * $24 \times \tau \left({24}\right) = 192 = 32 \times \tau \left({32}\right)$

Also see