# Quintuplets of Consecutive Integers which are not Sigma Values

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## Theorem

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

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

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

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

## Proof

## Sources

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