# 140

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## 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 $\tau \left({n}\right) \mathrel \backslash \phi \left({n}\right) \mathrel \backslash \sigma \left({n}\right)$:
$\tau \left({140}\right) = 12$, $\phi \left({140}\right) = 48$, $\sigma \left({140}\right) = 336$