Quintuplets of Consecutive Integers which are not Divisor Sum Values

Theorem

The elements of the following $5$-tuples of consecutive integers have the property that they are not values of the divisor sum function $\map {\sigma_1} n$ for any $n$:

$\tuple {49, 50, 51, 52, 53}$

$\tuple {115, 116, 117, 118, 119}$

$\tuple {145, 146, 147, 148, 149}$

Proof

This theorem requires a proof. In particular: Can be done by listing all $\sigma_1$s less than the numbers concerned, which is tedious You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. 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 {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $49$