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%I #28 Jul 31 2021 17:03:35
%S 1375298099,1419138368,2370099168,5839897526,16681039431,27326512069,
%T 28461637018,34090335168,44009539168,45412427776,47166830151,
%U 57788232400,75843173376,89516861675,89636142881,140201053499,186876720832,191701358025,209797492893,220333644849
%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 (Python)
%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)):
%o print(rets[x])
%Y Cf. A003348, A309762, A344644.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 14 2021
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