%N Numbers that are the sum of three fifth powers in two or more ways.
%C No numbers that are the sum of three fifth powers in three ways have been found. As a result, there is no corresponding sequence for the sum of three fifth powers in exactly two ways.
%H David Consiglio, Jr., <a href="/A345010/b345010.txt">Table of n, a(n) for n = 1..396</a>
%e 1419138368 is a term because 1419138368 = 13^5 + 51^5 + 64^5 = 18^5 + 44^5 + 66^5.
%o from itertools import combinations_with_replacement as cwr
%o from collections import defaultdict
%o keep = defaultdict(lambda: 0)
%o power_terms = [x**5 for x in range(1, 1000)]
%o for pos in cwr(power_terms, 3):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v >= 2])
%o for x in range(len(rets)):
%Y Cf. A003348, A309762, A344644.
%A _David Consiglio, Jr._, Jun 14 2021