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A344644 Numbers that are the sum of four fifth powers in two or more ways.

%I A344644 #6 Jul 31 2021 17:02:43
%S A344644 51445,876733,1646240,3558289,4062500,5687000,7962869,8227494,9792364,
%T A344644 9924675,10908544,12501135,15249850,18317994,18804544,20611151,
%U A344644 20983875,21297837,23944908,24201342,24598407,27806867,28055456,29480343,31584102,32557875,32814683,35469555,40882844,45177175
%N A344644 Numbers that are the sum of four fifth powers in two or more ways.
%H A344644 David Consiglio, Jr., <a href="/A344644/b344644.txt">Table of n, a(n) for n = 1..20000</a>
%e A344644 1646240 is a term because 1646240 = 9^5 + 15^5 + 15^5 + 15^5 = 11^5 + 13^5 + 13^5 + 17^5
%o A344644 (Python)
%o A344644 from itertools import combinations_with_replacement as cwr
%o A344644 from collections import defaultdict
%o A344644 keep = defaultdict(lambda: 0)
%o A344644 power_terms = [x**5 for x in range(1, 500)]
%o A344644 for pos in cwr(power_terms, 4):
%o A344644     tot = sum(pos)
%o A344644     keep[tot] += 1
%o A344644 rets = sorted([k for k, v in keep.items() if v >= 2])
%o A344644 for x in range(len(rets)):
%o A344644     print(rets[x])
%Y A344644 Cf. A003349, A309763, A342685, A344645, A345010, A345337.
%K A344644 nonn
%O A344644 1,1
%A A344644 _David Consiglio, Jr._, May 25 2021