Background
A Ruth-Aaron pair is a pair of consecutive positive integers n
and 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 714=2*3*7*17
, 715=5*11*13
, and 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 715
th home run. You can learn more about the fascinating history of these numbers in this Numberphile video.
Goal
Write a complete program or function which, given a positive integer n
, outputs the n
th Aaron number, where the n
th number is defined to be the larger integer of the n
th Ruth-Aaron pair. Thus the n
th Aaron number is a(n)+1
, where a(n)
is the n
th term in the OEIS sequence A039752.
Test cases
The first few Aaron numbers are
6,9,16,78,126,715,949,1331,1521,1863,2492,3249,4186,4192,5406,5561,5960,6868,8281,8464,10648,12352,14588,16933,17081,18491,20451,24896,26643,26650,28449,28810,33020,37829,37882,41262,42625,43216
Rules
Standard loopholes are forbidden.
Input and output may be in any convenient format.
This is code-golf, the shortest answer (in bytes) wins.