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A345722 Numbers that are the sum of six fifth powers in eight or more ways.

%I A345722 #6 Jul 31 2021 16:37:46
%S A345722 2295937600,4335900525,6251954544,8986552608,9085584992,13413708308,
%T A345722 14539246326,15277569450,15728636000,16770321920,16873011232,
%U A345722 16933805856,17572402769,17713454592,17960776999,18190647200,19621666592,20570070125,20827689300
%N A345722 Numbers that are the sum of six fifth powers in eight or more ways.
%H A345722 Sean A. Irvine, <a href="/A345722/b345722.txt">Table of n, a(n) for n = 1..389</a>
%e A345722 4335900525 is a term because 4335900525 = 2^5 + 24^5 + 34^5 + 56^5 + 61^5 + 78^5 = 3^5 + 21^5 + 37^5 + 54^5 + 62^5 + 78^5 = 3^5 + 21^5 + 39^5 + 49^5 + 66^5 + 77^5 = 3^5 + 26^5 + 32^5 + 49^5 + 72^5 + 73^5 = 8^5 + 16^5 + 42^5 + 49^5 + 61^5 + 79^5 = 9^5 + 13^5 + 43^5 + 47^5 + 66^5 + 77^5 = 19^5 + 20^5 + 30^5 + 45^5 + 61^5 + 80^5 = 21^5 + 24^5 + 28^5 + 37^5 + 67^5 + 78^5.
%o A345722 (Python)
%o A345722 from itertools import combinations_with_replacement as cwr
%o A345722 from collections import defaultdict
%o A345722 keep = defaultdict(lambda: 0)
%o A345722 power_terms = [x**5 for x in range(1, 1000)]
%o A345722 for pos in cwr(power_terms, 6):
%o A345722     tot = sum(pos)
%o A345722     keep[tot] += 1
%o A345722     rets = sorted([k for k, v in keep.items() if v >= 8])
%o A345722     for x in range(len(rets)):
%o A345722         print(rets[x])
%Y A345722 Cf. A345565, A345630, A345721, A345723, A346363.
%K A345722 nonn
%O A345722 1,1
%A A345722 _David Consiglio, Jr._, Jun 24 2021