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%I A345174 #6 Aug 05 2021 15:25:38
%S A345174 2430,2979,3214,3249,3312,3492,3520,3737,3753,3788,3816,3842,3942,
%T A345174 3968,4121,4185,4213,4267,4355,4392,4411,4418,4446,4453,4456,4465,
%U A345174 4472,4482,4509,4544,4563,4600,4626,4663,4670,4723,4753,4896,4905,4915,4924,4938,4941
%N A345174 Numbers that are the sum of five third powers in six or more ways.
%H A345174 David Consiglio, Jr., <a href="/A345174/b345174.txt">Table of n, a(n) for n = 1..10000</a>
%e A345174 2430 is a term because 2430 = 1^3 + 2^3 + 2^3 + 5^3 + 12^3  = 1^3 + 3^3 + 4^3 + 7^3 + 11^3  = 2^3 + 2^3 + 6^3 + 6^3 + 11^3  = 2^3 + 3^3 + 3^3 + 9^3 + 10^3  = 3^3 + 5^3 + 8^3 + 8^3 + 8^3  = 3^3 + 4^3 + 7^3 + 8^3 + 9^3.
%o A345174 (Python)
%o A345174 from itertools import combinations_with_replacement as cwr
%o A345174 from collections import defaultdict
%o A345174 keep = defaultdict(lambda: 0)
%o A345174 power_terms = [x**3 for x in range(1, 1000)]
%o A345174 for pos in cwr(power_terms, 5):
%o A345174     tot = sum(pos)
%o A345174     keep[tot] += 1
%o A345174 rets = sorted([k for k, v in keep.items() if v >= 6])
%o A345174 for x in range(len(rets)):
%o A345174     print(rets[x])
%Y A345174 Cf. A343989, A344799, A344940, A345148, A345175, A345180, A345515.
%K A345174 nonn
%O A345174 1,1
%A A345174 _David Consiglio, Jr._, Jun 10 2021

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