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# Ruth–Aaron pair

#### Description

A Ruth-Aaron pair consists of two consecutive integers (e.g. 714 and 715) for which the sums of the prime factors of each integer are equal.

For example:

$$714 = 2 × 3 × 7 × 17$$

$$715 = 5 × 11 × 13$$

and the sum would be:

$$2 + 3 + 7 + 17 = 5 + 11 + 13 = 29$$

The first three Ruth-Aaron pairs are:

(5, 6), (8, 9), (15, 16)

#### Question

Find the lesser integer of the 15th Ruth-Aaron pair. For clarification: (a, b) is a Ruth-Aaron pair, find a

Find the lesser integer of the 15th Ruth-Aaron pair. For clarification: (a, b) is a Ruth-Aaron pair, find a