Ruth Aaron Numbers

As Ruth-Aaron figures referred to a pair of consecutive natural numbers whose prime factors have the same sum. There are two different definitions that differ in whether or not multiply occurring prime factors are counted according to their multiplicity.

Ruth Aaron numbers are named after the American baseball legends Babe Ruth and Hank Aaron . Babe Ruth scored 714 home runs in his career , a record that was not broken until 1974 - 39 years later - by Hank Aaron. When examining the pair of numbers 714/715, it turned out that their product is equal to the product of the first seven prime numbers:

${\displaystyle 714\cdot 715=2\cdot 3\cdot 5\cdot 7\cdot 11\cdot 13\cdot 17}$

In addition, the sum of the prime factors of 714 is equal to the sum of the prime factors of 715:

${\displaystyle 714=2\cdot 3\cdot 7\cdot 17}$

${\displaystyle 715=5\cdot 11\cdot 13}$

${\displaystyle 2+3+7+17=5+11+13}$

Web links

• Eric W. Weisstein : Ruth-Aaron couple . In: MathWorld (English).
• Follow A006145 in OEIS (English; Ruth Aaron numbers without multiples)
• Episode A039752 in OEIS (English; Ruth-Aaron numbers with multiples)