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A345150 Numbers that are the sum of four third powers in seven or more ways.

%I A345150 #7 Aug 05 2021 15:27:29
%S A345150 13104,18928,19376,20755,21203,21896,22743,24544,24570,24787,25172,
%T A345150 25928,27720,27755,27846,28917,29582,30429,31031,31248,31339,31402,
%U A345150 31528,32858,33579,34056,34624,34713,34776,35289,35317,35441,35497,35712,36162,36190,36225
%N A345150 Numbers that are the sum of four third powers in seven or more ways.
%H A345150 David Consiglio, Jr., <a href="/A345150/b345150.txt">Table of n, a(n) for n = 1..10000</a>
%e A345150 13104 is a term because 13104 = 1^3 + 10^3 + 16^3 + 18^3  = 1^3 + 11^3 + 14^3 + 19^3  = 2^3 + 9^3 + 15^3 + 19^3  = 4^3 + 6^3 + 14^3 + 20^3  = 4^3 + 9^3 + 10^3 + 21^3  = 5^3 + 7^3 + 11^3 + 21^3  = 8^3 + 9^3 + 14^3 + 19^3.
%o A345150 (Python)
%o A345150 from itertools import combinations_with_replacement as cwr
%o A345150 from collections import defaultdict
%o A345150 keep = defaultdict(lambda: 0)
%o A345150 power_terms = [x**3 for x in range(1, 1000)]
%o A345150 for pos in cwr(power_terms, 4):
%o A345150     tot = sum(pos)
%o A345150     keep[tot] += 1
%o A345150 rets = sorted([k for k, v in keep.items() if v >= 7])
%o A345150 for x in range(len(rets)):
%o A345150     print(rets[x])
%Y A345150 Cf. A025372, A344922, A345086, A345148, A345151, A345152, A345180.
%K A345150 nonn
%O A345150 1,1
%A A345150 _David Consiglio, Jr._, Jun 09 2021