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A345630 Numbers that are the sum of seven fifth powers in eight or more ways.

%I A345630 #6 Jul 31 2021 16:25:31
%S A345630 36620574,80552143,81401376,82078424,92347417,93653176,94486699,
%T A345630 94626949,98873875,105674625,110276376,121050874,124732805,125959393,
%U A345630 127808693,129228307,130298618,134581976,144209018,145340799,147245218,147898763,151727082
%N A345630 Numbers that are the sum of seven fifth powers in eight or more ways.
%H A345630 Sean A. Irvine, <a href="/A345630/b345630.txt">Table of n, a(n) for n = 1..10000</a>
%e A345630 80552143 is a term because 80552143 = 1^5 + 4^5 + 21^5 + 21^5 + 23^5 + 29^5 + 34^5 = 1^5 + 8^5 + 14^5 + 23^5 + 23^5 + 32^5 + 32^5 = 1^5 + 8^5 + 16^5 + 19^5 + 27^5 + 28^5 + 34^5 = 3^5 + 12^5 + 13^5 + 14^5 + 28^5 + 31^5 + 32^5 = 3^5 + 14^5 + 17^5 + 18^5 + 18^5 + 27^5 + 36^5 = 4^5 + 11^5 + 13^5 + 22^5 + 23^5 + 24^5 + 36^5 = 5^5 + 6^5 + 19^5 + 20^5 + 23^5 + 24^5 + 36^5 = 6^5 + 23^5 + 25^5 + 25^5 + 25^5 + 29^5 + 30^5.
%o A345630 (Python)
%o A345630 from itertools import combinations_with_replacement as cwr
%o A345630 from collections import defaultdict
%o A345630 keep = defaultdict(lambda: 0)
%o A345630 power_terms = [x**5 for x in range(1, 1000)]
%o A345630 for pos in cwr(power_terms, 7):
%o A345630     tot = sum(pos)
%o A345630     keep[tot] += 1
%o A345630     rets = sorted([k for k, v in keep.items() if v >= 8])
%o A345630     for x in range(len(rets)):
%o A345630         print(rets[x])
%Y A345630 Cf. A345574, A345616, A345629, A345631, A345722, A346285.
%K A345630 nonn
%O A345630 1,1
%A A345630 _David Consiglio, Jr._, Jun 22 2021