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A345619 Numbers that are the sum of nine fifth powers in two or more ways.

%I A345619 #6 Jul 31 2021 16:08:49
%S A345619 4101,4132,4163,4194,4225,4343,4374,4405,4436,4585,4616,4647,4827,
%T A345619 4858,5069,5124,5155,5186,5217,5366,5397,5428,5608,5639,5850,6147,
%U A345619 6178,6209,6389,6420,6631,7170,7201,7225,7256,7287,7318,7412,7467,7498,7529,7709,7740
%N A345619 Numbers that are the sum of nine fifth powers in two or more ways.
%H A345619 Sean A. Irvine, <a href="/A345619/b345619.txt">Table of n, a(n) for n = 1..10000</a>
%e A345619 4132 is a term because 4132 = 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 4^5 = 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5.
%o A345619 (Python)
%o A345619 from itertools import combinations_with_replacement as cwr
%o A345619 from collections import defaultdict
%o A345619 keep = defaultdict(lambda: 0)
%o A345619 power_terms = [x**5 for x in range(1, 1000)]
%o A345619 for pos in cwr(power_terms, 9):
%o A345619     tot = sum(pos)
%o A345619     keep[tot] += 1
%o A345619     rets = sorted([k for k, v in keep.items() if v >= 2])
%o A345619     for x in range(len(rets)):
%o A345619         print(rets[x])
%Y A345619 Cf. A003354, A345586, A345610, A345620, A345634, A346337.
%K A345619 nonn
%O A345619 1,1
%A A345619 _David Consiglio, Jr._, Jun 20 2021