Integers whose Divisor Sum is Cube
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Theorem
The following positive integers are those whose divisor sum is a cube:
- $1, 7, 102, 110, 142, 159, 187, 381, 690, 714, 770, 994, 1034, \ldots$
This sequence is A020477 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Examples
| \(\ds \map {\sigma_1} 1\) | \(=\) | \(\, \ds 1 \, \) | \(\, \ds = \, \) | \(\ds 1^3\) | $\sigma_1$ 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
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $110$