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A345720 Numbers that are the sum of six fifth powers in six or more ways.

%I A345720 #9 Jul 31 2021 16:37:39
%S A345720 287718651,553545456,746783675,972232800,1005620508,1040741042,
%T A345720 1070652352,1074892544,1182426366,1184966816,1197332400,1243267146,
%U A345720 1317183650,1364866263,1387455091,1429663400,1498160992,1529189818,1554833117,1558594400,1610298901
%N A345720 Numbers that are the sum of six fifth powers in six or more ways.
%H A345720 Sean A. Irvine, <a href="/A345720/b345720.txt">Table of n, a(n) for n = 1..10000</a>
%e A345720 553545456 is a term because 553545456 = 1^5 + 14^5 + 20^5 + 24^5 + 47^5 + 50^5 = 4^5 + 14^5 + 37^5 + 42^5 + 43^5 + 46^5 = 4^5 + 26^5 + 29^5 + 34^5 + 42^5 + 51^5 = 9^5 + 15^5 + 22^5 + 22^5 + 33^5 + 55^5 = 9^5 + 26^5 + 29^5 + 32^5 + 37^5 + 53^5 = 12^5 + 24^5 + 27^5 + 32^5 + 38^5 + 53^5.
%o A345720 (Python)
%o A345720 from itertools import combinations_with_replacement as cwr
%o A345720 from collections import defaultdict
%o A345720 keep = defaultdict(lambda: 0)
%o A345720 power_terms = [x**5 for x in range(1, 1000)]
%o A345720 for pos in cwr(power_terms, 6):
%o A345720     tot = sum(pos)
%o A345720     keep[tot] += 1
%o A345720     rets = sorted([k for k, v in keep.items() if v >= 6])
%o A345720     for x in range(len(rets)):
%o A345720         print(rets[x])
%Y A345720 Cf. A345563, A345609, A345719, A345721, A345864, A346361.
%K A345720 nonn
%O A345720 1,1
%A A345720 _David Consiglio, Jr._, Jun 24 2021