# 140

Jump to navigation
Jump to search

## 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 $1, 6, 28$:
- $\dfrac {140 \times \map \tau {140} } {\map \sigma {140} } = 5$

- and the $3$rd after $1, 6$ whose divisors also have an arithmetic mean which is an integer:
- $\dfrac {\map \sigma {140} } {\map \tau {140} } = 28$

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

## Also see

*Previous ... Next*: Sequence of Numbers with Integer Arithmetic and Harmonic Means of Divisors*Previous ... Next*: Ore Number*Previous ... Next*: Quasiamicable Numbers*Previous ... Next*: Square Pyramidal Number*Previous ... Next*: Numbers such that Tau divides Phi divides Sigma

## Sources

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $140$