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 $\map \sigma n$ for any $n$:


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


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


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