# 140

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## Number

$140$ (one hundred and forty) is:

$2^2 \times 5 \times 7$

With $195$, an element of the $2$nd quasiamicable pair:
$\map {\sigma_1} {140} = \map {\sigma_1} {195} = 336 = 140 + 195 + 1$

The $4$th Ore number after $1, 6, 28$:
$\dfrac {140 \times \map {\sigma_0} {140} } {\map {\sigma_1} {140} } = 5$
and the $3$rd after $1, 6$ whose divisors also have an arithmetic mean which is an integer:
$\dfrac {\map {\sigma_1} {140} } {\map {\sigma_0} {140} } = 28$

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

The $10$th integer $n$ after $1, 3, 15, 30, 35, 56, 70, 78, 105$ with the property that $\map {\sigma_0} n \divides \map \phi n \divides \map {\sigma_1} n$:
$\map {\sigma_0} {140} = 12$, $\map \phi {140} = 48$, $\map {\sigma_1} {140} = 336$

### Arithmetic Functions on $140$

 $\ds \map {\sigma_0} { 140 }$ $=$ $\ds 12$ $\sigma_0$ of $140$ $\ds \map \phi { 140 }$ $=$ $\ds 48$ $\phi$ of $140$ $\ds \map {\sigma_1} { 140 }$ $=$ $\ds 336$ $\sigma_1$ of $140$