# 192

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## Number

$192$ (one hundred and ninety-two) is:

$2^6 \times 3$

The $1$st of $4$ integers $n$ such that $n + 2 n$ can be expressed as a sum using each of the digits $1$ to $9$ exactly once each:
$192 + 384 = 576$

The $2$nd positive integer after $128$ with $7$ or more prime factors:
$192 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3$

The $2$nd element of the $1$st set of $3$ integers $T$ such that $m \map {\sigma_0} m$ is equal for each $m \in T$:
$168 \times \map {\sigma_0} {168} = 192 \times \map {\sigma_0} {192} = 224 \times \map {\sigma_0} {224} = 2688$

The $6$th positive integer after $64$, $96$, $128$, $144$, $160$ with $6$ or more prime factors:
$192 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3$

The $31$st happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $91$, $94$, $97$, $100$, $103$, $109$, $129$, $130$, $133$, $139$, $167$, $176$, $188$, $190$:
$192 \to 1^2 + 9^2 + 2^2 = 1 + 81 + 4 = 86 \to 8^2 + 6^2 = 64 + 36 = 100 \to 1^2 + 0^2 + 0^2 = 1$

The $38$th positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.