70

Number
$70$ (seventy) is:


 * $2 \times 5 \times 7$


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


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


 * The $4$th sphenic number after $30$, $42$, $66$:
 * $70 = 2 \times 5 \times 7$


 * The $4$th central binomial coefficient after $2$, $6$, $20$:
 * $70 = \dbinom {2 \times 4} 4 := \dfrac {8!} {\paren {4!}^2}$


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


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


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


 * The $7$th integer $n$ after $1$, $3$, $15$, $30$, $35$, $56$ with the property that $\map \tau n \divides \map \phi n \divides \map \sigma n$:
 * $\map \tau {70} = 8$, $\map \phi {70} = 24$, $\map \sigma {70} = 144$


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


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

Also see

 * Tau Function of 70