# Integers whose Divisor Sum is Cube/Examples

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## 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): $714$