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 $\sigma$ function $\sigma \left({n}\right)$ for any $n$:


 * $\left({49, 50, 51, 52, 53}\right)$


 * $\left({115, 116, 117, 118, 119}\right)$


 * $\left({145, 146, 147, 148, 149}\right)$