Integers whose Divisor Sum is Cube/Examples

Examples of Integers whose Divisor Sum is Cube

The following positive integers are those whose divisor sum is a cube:

$1, 7, 102, 110, 142, 159, 187, 381, 690, 714, 770, 994, 1034, \ldots$

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$\ds \map {\sigma_1} 1$

$=$

$\, \ds 1 \, $

$\, \ds = \, $

$\ds 1^3$

$\sigma_1$ of $1$

$\ds \map {\sigma_1} 7$

$=$

$\, \ds 8 \, $

$\, \ds = \, $

$\ds 2^3$

Divisor Sum of Prime Number

$\ds \map {\sigma_1} {102}$

$=$

$\, \ds 216 \, $

$\, \ds = \, $

$\ds 6^3$

$\sigma_1$ of $102$

$\ds \map {\sigma_1} {110}$

$=$

$\, \ds 216 \, $

$\, \ds = \, $

$\ds 6^3$

$\sigma_1$ of $110$

$\ds \map {\sigma_1} {714}$

$=$

$\, \ds 1728 \, $

$\, \ds = \, $

$\ds 12^3$

$\sigma_1$ of $714$

Sources

1974: C. Nelson, D.E. Penney and C. Pomerance: 714 and 715 (J. Recr. Math. Vol. 7, no. 2: pp. 87 – 89)
1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $714$
1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $110$
1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $714$