70

Number
$70$ (seventy) is:


 * $2 \times 5 \times 7$


 * The $2$nd primitive abundant number after $20$:
 * $1 + 2 + 5 + 7 + 10 + 14 + 35 = 74 > 70$


 * The $7$th pentagonal number after $1, 5, 12, 22, 35, 51$:
 * $70 = 1 + 4 + 7 + 10 + 13 + 16 + 19 = \dfrac {7 \left({3 \times 7 - 1}\right)} 2$


 * The $13$th generalized pentagonal number after $1, 2, 5, 7, 12, 15, 22, 26, 35, 40, 51, 57$:
 * $70 = \dfrac {7 \left({3 \times 7 - 1}\right)} 2$


 * The $5$th pentatope number after $1, 5, 15, 35$:
 * $70 = 1 + 4 + 10 + 20 + 35 = \dfrac {5 \left({5 + 1}\right) \left({5 + 2}\right) \left({5 + 3}\right)} {24}$


 * The $13$th happy number after $1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68$:
 * $70 \to 7^2 + 0^2 = 49 \to 4^2 + 9^2 = 16 + 81 = 97 \to 9^2 + 7^2 = 81 + 49 = 130 \to 1^2 + 3^2 + 0^2 = 1 + 9 + 0 = 10 \to 1^2 + 0^2 = 1$


 * The $5$th number after $1, 3, 22, 66$ whose $\sigma$ value is square:


 * The $9$th integer after $7, 13, 19, 35, 38, 41, 57, 65$ the decimal representation of whose square can be split into two parts which are each themselves square:
 * $70^2 = 4900; 4 = 2^2, 900 = 30^2$


 * The $1$st weird number:
 * $\sigma \left({70}\right) = 74$: its aliquot parts are $1, 2, 5, 7, 10, 14, 35$, from which $70$ cannot be made.


 * The $7$th integer $n$ after $1, 3, 15, 30, 35, 56$ with the property that $\tau \left({n}\right) \mathrel \backslash \phi \left({n}\right) \mathrel \backslash \sigma \left({n}\right)$:
 * $\tau \left({70}\right) = 8$, $\phi \left({70}\right) = 24$, $\sigma \left({70}\right) = 144$

Also see