A Ruth-Aaron pair is a pair of consecutive positive integers
n+1 such that the sum of the prime factors (counting repeated prime factors) of each integer are equal. For example,
(714,715) is a Ruth-Aaron pair, since
2+3+7+17=5+11+13=29. The name Ruth-Aaron pair was chosen by Carl Pomerance in reference to Babe Ruth's career home run total of
714, which stood as the world record from May 25, 1935 until April 8, 1974 when Hank Aaron hit his
715th home run. You can learn more about the fascinating history of these numbers in this Numberphile video.
Write a complete program or function which, given a positive integer
n, outputs the
nth Aaron number, where the
nth number is defined to be the larger integer of the
nth Ruth-Aaron pair. Thus the
nth Aaron number is
a(n) is the
nth term in the OEIS sequence A039752.
The first few Aaron numbers are