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 A345010 Numbers that are the sum of three fifth powers in two or more ways. 4

%I

%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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Last modified January 23 03:15 EST 2022. Contains 350504 sequences. (Running on oeis4.)