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 $140$

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 Divisor Count divides Phi divides Divisor Sum

Sources

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