A '''Ruth–Aaron''' pair consists of two consecutive integers (e.g., 714 and 715) for which the sums of the prime divisors of each integer are equal. So called because 714 is Babe Ruth's lifetime home run record; Hank Aaron's 715th home run broke this record and 714 and 715 have the same prime divisor sum.


A '''Ruth–Aaron''' triple consists of '''''three''''' consecutive integers with the same properties.


There is a second variant of '''Ruth–Aaron''' numbers, one which uses prime ''factors'' rather than prime ''divisors''. The difference; divisors are unique, factors may be repeated. The 714, 715 pair appears in both, so the name still fits. 


It is common to refer to each '''Ruth–Aaron''' group by the first number in it. 


;Task

* Find and show, here on this page, the first '''30''' '''Ruth-Aaron numbers''' (factors).

* Find and show, here on this page, the first '''30''' '''Ruth-Aaron numbers''' (divisors).


;Stretch

* Find and show the first '''Ruth-Aaron triple''' (factors).

* Find and show the first '''Ruth-Aaron triple''' (divisors).


;See also

;*[[wp:Ruth–Aaron_pair|Wikipedia: Ruth–Aaron pair]]
;*[[oeis:A006145|OEIS:A006145 - Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1]]
;*[[oeis:A039752|OEIS:A039752 - Ruth-Aaron numbers (2): sum of prime divisors of n = sum of prime divisors of n+1 (both taken with multiplicity)]]

