### Ruth-Aaron Pairs

MathBabbler decided to create this Ruth-Aaron pair collection after posting nBABs for the numbers 153 and 154, which just happen to be a Ruth-Aaron pair.

From OEIS.org: Ruth-Aaron pair if "sum of prime divisors of n = sum of prime divisors of n+1."

The first few Ruth-Aaron pairs...

```   If only distinct prime factors are used:

(5, 6), (24, 25), (49, 50), (77, 78), (104, 105), (153, 154),
(369, 370), (492, 493), (714, 715), (1682, 1683), (2107, 2108),
..., (2600, 2601), ...

If repeated prime factors are used:

(5, 6), (8, 9), (15, 16), (77, 78), (125, 126), (714, 715),
(948, 949), (1330, 1331), (1520, 1521), (1862, 1863),
(2491, 2492), (3248, 3249), (4185, 4186), (4191, 4192)...
```

The following checks to confirm that 153 and 154 are a Ruth-Aaron pair.

```   prime factors of 153:  3, 3, 17
prime factors of 154:  2, 7, 11

sum distinct prime factors of 153:  3 + 17 = 20
sum distinct prime factors of 154:  2 + 7 + 11 = 20
```

OEIS.org::id:A006145

BAB::Ruth-Aaron Pairs [31 March 2009]

##### Added In 2015
(21183, 21184)

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 10 July 2009
``` + added (2600, 2601) on 08 December 2009 + added (1862, 1863) on 24 February 2010 + added (369, 370) on 29 June 2010 + added (1682, 1683) on 25 August 2014 + added (21183, 21184) on 04 April 2015 + added (492, 493) on 07 June 2018 + added (492, 493) on 08 June 2018 ```

This work is licensed under a Creative Commons Attribution 3.0 United States License.