# 16

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## Number

$16$ (sixteen) is:

$2^4$

The $4$th square number after $1$, $4$, $9$:
$16 = 4 \times 4$

The $5$th powerful number after $1$, $4$, $8$, $9$

The $2$nd fourth power after $1$:
$16 = 2 \times 2 \times 2 \times 2$

The $2$nd power of $4$ after $(1)$, $4$:
$16 = 4^2$

The $1$st power of $16$ after the zeroth $1$:
$16 = 16^1$

The $9$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $12$:
$\sigma \left({16}\right) = 31$

The $9$th Ulam number after $1$, $2$, $3$, $4$, $6$, $8$, $11$, $13$:
$16 = 3 + 13$

The $1$st square number to be the sum of two triangular numbers in two different ways:
$16 = 10 + 6 = 15 + 1$

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

The $5$th almost perfect number after $1$, $2$, $4$, $8$:
$\sigma \left({16}\right) = 31 = 2 \times 16 - 1$

The $6$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
$3$, $4$, $9$, $10$, $12$, $16$, $\ldots$

The $8$th even number after $2$, $4$, $6$, $8$, $10$, $12$, $14$ which cannot be expressed as the sum of $2$ composite odd numbers.

The $11$th after $1$, $2$, $4$, $5$, $6$, $8$, $9$, $12$, $13$, $15$ of the $24$ positive integers which cannot be expressed as the sum of distinct non-pythagorean primes.

The $14$th integer $n$ after $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $13$, $14$, $15$ such that $2^n$ contains no zero in its decimal representation:
$2^{16} = 65 \, 536$

The $11$th positive integer after $2$, $3$, $4$, $7$, $8$, $9$, $10$, $11$, $14$, $15$ which cannot be expressed as the sum of distinct pentagonal numbers.

The $4$th square after $1$, $4$, $9$ which has no more than $2$ distinct digits