140

Number
$140$ (one hundred and forty) is:


 * $2^2 \times 5 \times 7$


 * The $4$th Ore number after $1, 6, 28$:
 * $\dfrac {140 \times \tau \left({140}\right)} {\sigma \left({140}\right)} = 5$
 * and the $3$rd after $1, 6$ whose divisors also have an arithmetic mean which is an integer:
 * $\dfrac {\sigma \left({140}\right)} {\tau \left({140}\right)} = 28$


 * The $7$th square pyramidal number after $1, 5, 14, 30, 55, 91$:
 * $140 = 1 + 4 + 9 + 16 + 25 + 36 + 49$


 * With $195$, an element of the $2$nd quasiamicable pair:
 * $\sigma \left({140}\right) = \sigma \left({195}\right) = 336 = 140 + 195 + 1$


 * The $10$th integer $n$ after $1, 3, 15, 30, 35, 56, 70, 78, 105$ with the property that $\tau \left({n}\right) \mathrel \backslash \phi \left({n}\right) \mathrel \backslash \sigma \left({n}\right)$:
 * $\tau \left({140}\right) = 12$, $\phi \left({140}\right) = 48$, $\sigma \left({140}\right) = 336$