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A345638 Numbers that are the sum of ten fifth powers in six or more ways.

%I A345638 #6 Jul 31 2021 15:58:41
%S A345638 392095,392306,399839,406802,407583,434676,491643,492063,520261,
%T A345638 521106,538323,538534,540927,553325,555098,563526,582089,592398,
%U A345638 608190,611072,614196,637833,639903,640715,640895,640926,640957,641106,643671,653523,655327,656616
%N A345638 Numbers that are the sum of ten fifth powers in six or more ways.
%H A345638 Sean A. Irvine, <a href="/A345638/b345638.txt">Table of n, a(n) for n = 1..10000</a>
%e A345638 392306 is a term because 392306 = 1^5 + 1^5 + 1^5 + 3^5 + 3^5 + 8^5 + 9^5 + 10^5 + 10^5 + 10^5 = 1^5 + 1^5 + 2^5 + 4^5 + 4^5 + 7^5 + 8^5 + 8^5 + 9^5 + 12^5 = 1^5 + 2^5 + 3^5 + 3^5 + 4^5 + 5^5 + 8^5 + 8^5 + 11^5 + 11^5 = 2^5 + 2^5 + 3^5 + 3^5 + 3^5 + 6^5 + 7^5 + 9^5 + 9^5 + 12^5 = 2^5 + 2^5 + 3^5 + 4^5 + 4^5 + 4^5 + 6^5 + 9^5 + 11^5 + 11^5 = 2^5 + 2^5 + 3^5 + 4^5 + 5^5 + 5^5 + 5^5 + 8^5 + 10^5 + 12^5.
%o A345638 (Python)
%o A345638 from itertools import combinations_with_replacement as cwr
%o A345638 from collections import defaultdict
%o A345638 keep = defaultdict(lambda: 0)
%o A345638 power_terms = [x**5 for x in range(1, 1000)]
%o A345638 for pos in cwr(power_terms, 10):
%o A345638     tot = sum(pos)
%o A345638     keep[tot] += 1
%o A345638     rets = sorted([k for k, v in keep.items() if v >= 6])
%o A345638     for x in range(len(rets)):
%o A345638         print(rets[x])
%Y A345638 Cf. A345599, A345623, A345637, A345639, A346351.
%K A345638 nonn
%O A345638 1,1
%A A345638 _David Consiglio, Jr._, Jun 20 2021