140

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


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


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


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


 * 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 $\map {\sigma_0} n \divides \map \phi n \divides \map \sigma n$:
 * $\map {\sigma_0} {140} = 12$, $\map \phi {140} = 48$, $\map \sigma {140} = 336$