Integers whose Divisor Sum is Cube/Examples
Jump to navigation
Jump to search
Examples of Integers whose Divisor Sum is Cube
The following positive integers are those whose divisor sum is a cube:
- $1, 7, 102, 110, 142, 159, 187, 381, 690, 714, 770, 994, 1034, \ldots$
 | This page has been identified as a candidate for refactoring of basic complexity. In particular: Extract these into separate Examples pages Until this has been finished, please leave {{Refactor}} in the code.
New contributors: Refactoring is a task which is expected to be undertaken by experienced editors only. Because of the underlying complexity of the work needed, it is recommended that you do not embark on a refactoring task until you have become familiar with the structural nature of pages of $\mathsf{Pr} \infty \mathsf{fWiki}$.To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Refactor}} from the code. |
| \(\ds \map {\sigma_1} 1\) | \(=\) | \(\, \ds 1 \, \) | \(\, \ds = \, \) | \(\ds 1^3\) | $\sigma_1$ 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): $714$