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A345626 Numbers that are the sum of nine fifth powers in nine or more ways.

%I A345626 #9 Jul 31 2021 16:09:49
%S A345626 1969221,2596936,3353186,3378178,3923426,3981447,4094027,4096729,
%T A345626 4112329,4114188,4129465,4137209,4147736,4157156,4170112,4172994,
%U A345626 4254304,4303773,4410482,4475846,4477936,4483379,4485480,4492410,4501441,4510461,4543232,4652011,4691855
%N A345626 Numbers that are the sum of nine fifth powers in nine or more ways.
%H A345626 Sean A. Irvine, <a href="/A345626/b345626.txt">Table of n, a(n) for n = 1..10000</a>
%e A345626 2596936 is a term because 2596936 = 1^5 + 1^5 + 4^5 + 5^5 + 9^5 + 13^5 + 13^5 + 13^5 + 17^5 = 1^5 + 1^5 + 5^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 + 17^5 = 1^5 + 4^5 + 7^5 + 7^5 + 7^5 + 9^5 + 9^5 + 14^5 + 18^5 = 1^5 + 5^5 + 6^5 + 6^5 + 8^5 + 9^5 + 9^5 + 14^5 + 18^5 = 2^5 + 3^5 + 4^5 + 4^5 + 7^5 + 12^5 + 13^5 + 14^5 + 17^5 = 2^5 + 5^5 + 5^5 + 6^5 + 6^5 + 6^5 + 15^5 + 15^5 + 16^5 = 3^5 + 3^5 + 5^5 + 6^5 + 7^5 + 9^5 + 12^5 + 13^5 + 18^5 = 4^5 + 4^5 + 4^5 + 5^5 + 6^5 + 11^5 + 11^5 + 13^5 + 18^5 = 4^5 + 4^5 + 4^5 + 7^5 + 7^5 + 8^5 + 9^5 + 16^5 + 17^5.
%o A345626 (Python)
%o A345626 from itertools import combinations_with_replacement as cwr
%o A345626 from collections import defaultdict
%o A345626 keep = defaultdict(lambda: 0)
%o A345626 power_terms = [x**5 for x in range(1, 1000)]
%o A345626 for pos in cwr(power_terms, 9):
%o A345626     tot = sum(pos)
%o A345626     keep[tot] += 1
%o A345626     rets = sorted([k for k, v in keep.items() if v >= 9])
%o A345626     for x in range(len(rets)):
%o A345626         print(rets[x])
%Y A345626 Cf. A345593, A345617, A345625, A345627, A345641, A346344.
%K A345626 nonn
%O A345626 1,1
%A A345626 _David Consiglio, Jr._, Jun 20 2021