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A345631 Numbers that are the sum of seven fifth powers in nine or more ways.

%I A345631 #6 Jul 31 2021 16:25:36
%S A345631 110276376,124732805,127808693,130298618,134581976,188116743,
%T A345631 189642309,202274051,202686274,203343582,219063107,230909843,
%U A345631 233137574,233549568,234250752,235438301,244250335,251138524,252277376,253480833,254017026,254380543
%N A345631 Numbers that are the sum of seven fifth powers in nine or more ways.
%H A345631 Sean A. Irvine, <a href="/A345631/b345631.txt">Table of n, a(n) for n = 1..10000</a>
%e A345631 124732805 is a term because 124732805 = 3^5 + 18^5 + 22^5 + 22^5 + 24^5 + 27^5 + 39^5 = 4^5 + 15^5 + 17^5 + 21^5 + 29^5 + 34^5 + 35^5 = 5^5 + 14^5 + 17^5 + 24^5 + 25^5 + 35^5 + 35^5 = 7^5 + 8^5 + 17^5 + 26^5 + 29^5 + 34^5 + 34^5 = 7^5 + 10^5 + 12^5 + 31^5 + 31^5 + 32^5 + 32^5 = 7^5 + 12^5 + 23^5 + 24^5 + 24^5 + 26^5 + 39^5 = 7^5 + 14^5 + 22^5 + 22^5 + 23^5 + 28^5 + 39^5 = 16^5 + 25^5 + 25^5 + 28^5 + 28^5 + 28^5 + 35^5 = 20^5 + 24^5 + 24^5 + 25^5 + 25^5 + 32^5 + 35^5.
%o A345631 (Python)
%o A345631 from itertools import combinations_with_replacement as cwr
%o A345631 from collections import defaultdict
%o A345631 keep = defaultdict(lambda: 0)
%o A345631 power_terms = [x**5 for x in range(1, 1000)]
%o A345631 for pos in cwr(power_terms, 7):
%o A345631     tot = sum(pos)
%o A345631     keep[tot] += 1
%o A345631     rets = sorted([k for k, v in keep.items() if v >= 9])
%o A345631     for x in range(len(rets)):
%o A345631         print(rets[x])
%Y A345631 Cf. A345575, A345617, A345630, A345643, A345723, A346286.
%K A345631 nonn
%O A345631 1,1
%A A345631 _David Consiglio, Jr._, Jun 22 2021