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A345616 Numbers that are the sum of eight fifth powers in eight or more ways.

%I A345616 #6 Jul 31 2021 16:17:25
%S A345616 8625619,8742208,9773236,10036233,10071050,12247994,13180706,13377868,
%T A345616 13662501,14584992,14591744,14611077,15251119,15539667,16112362,
%U A345616 16374250,16391025,16472544,16588000,16667851,17059075,17216298,17405300,17917097,18107564,18392902
%N A345616 Numbers that are the sum of eight fifth powers in eight or more ways.
%H A345616 Sean A. Irvine, <a href="/A345616/b345616.txt">Table of n, a(n) for n = 1..100</a>
%e A345616 8742208 is a term because 8742208 = 1^5 + 1^5 + 2^5 + 3^5 + 5^5 + 7^5 + 15^5 + 24^5 = 1^5 + 1^5 + 9^5 + 9^5 + 11^5 + 17^5 + 18^5 + 22^5 = 1^5 + 3^5 + 7^5 + 12^5 + 12^5 + 13^5 + 17^5 + 23^5 = 2^5 + 5^5 + 6^5 + 7^5 + 15^5 + 15^5 + 15^5 + 23^5 = 3^5 + 3^5 + 7^5 + 9^5 + 12^5 + 12^5 + 21^5 + 21^5 = 4^5 + 4^5 + 4^5 + 11^5 + 11^5 + 12^5 + 21^5 + 21^5 = 4^5 + 4^5 + 8^5 + 8^5 + 9^5 + 15^5 + 17^5 + 23^5 = 8^5 + 13^5 + 14^5 + 14^5 + 14^5 + 16^5 + 19^5 + 20^5 = 10^5 + 12^5 + 12^5 + 13^5 + 16^5 + 16^5 + 19^5 + 20^5.
%o A345616 (Python)
%o A345616 from itertools import combinations_with_replacement as cwr
%o A345616 from collections import defaultdict
%o A345616 keep = defaultdict(lambda: 0)
%o A345616 power_terms = [x**5 for x in range(1, 1000)]
%o A345616 for pos in cwr(power_terms, 8):
%o A345616     tot = sum(pos)
%o A345616     keep[tot] += 1
%o A345616     rets = sorted([k for k, v in keep.items() if v >= 8])
%o A345616     for x in range(len(rets)):
%o A345616         print(rets[x])
%Y A345616 Cf. A345583, A345615, A345617, A345625, A345630, A346333.
%K A345616 nonn
%O A345616 1,1
%A A345616 _David Consiglio, Jr._, Jun 20 2021