42

Number
$42$ (forty-two) is:


 * $2 \times 3 \times 7$


 * The $5$th Catalan number after $(1,) \, 1, 2, 5, 14$:
 * $\dfrac 1 {5 + 1} \dbinom {2 \times 5} 5 = \dfrac 1 6 \times 252 = 42$


 * The $8$th abundant number after $12, 18, 20, 24, 30, 36, 40$:
 * $1 + 2 + 3 + 6 + 7 + 14 + 21 = 54 > 42$


 * The $10$th semiperfect number after $6, 12, 18, 20, 24, 28, 30, 36, 40$:
 * $42 = 7 + 14 + 21$


 * The $15$th highly abundant number after $1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36$:
 * $\sigma \left({42}\right) = 96$


 * The $4$th and largest positive integer after $1, 3, 14$ of which the product of its Euler $\phi$ function and its $\tau$ function equals its $\sigma$ function:
 * $\phi \left({42}\right) \tau \left({42}\right) = 12 \times 8 = 96 = \sigma \left({42}\right)$


 * The $8$th positive integer $n$ after $5, 11, 17, 23, 29, 30, 36$ such that no factorial of an integer can end with $n$ zeroes.


 * The $25$th positive integer after $2, 3, 4, 7, 8, \ldots, 26, 29, 30, 31, 32, 33, 37, 38$ which cannot be expressed as the sum of distinct pentagonal numbers.

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