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A345148 Numbers that are the sum of four third powers in six or more ways.

%I A345148 #7 Aug 05 2021 15:27:26
%S A345148 6883,12411,13104,13923,14112,14581,14896,14904,15561,15876,16317,
%T A345148 16640,17208,17479,17992,18739,18865,18928,19035,19080,19376,19665,
%U A345148 19712,19763,19880,20007,20384,20755,20979,21203,21231,21420,21707,21896,22409,22617,22743
%N A345148 Numbers that are the sum of four third powers in six or more ways.
%H A345148 David Consiglio, Jr., <a href="/A345148/b345148.txt">Table of n, a(n) for n = 1..10000</a>
%e A345148 6883 is a term because 6883 = 2^3 + 2^3 + 2^3 + 18^3  = 2^3 + 4^3 + 14^3 + 14^3  = 3^3 + 7^3 + 7^3 + 17^3  = 3^3 + 10^3 + 13^3 + 13^3  = 4^3 + 10^3 + 10^3 + 15^3  = 7^3 + 8^3 + 8^3 + 16^3.
%o A345148 (Python)
%o A345148 from itertools import combinations_with_replacement as cwr
%o A345148 from collections import defaultdict
%o A345148 keep = defaultdict(lambda: 0)
%o A345148 power_terms = [x**3 for x in range(1, 1000)]
%o A345148 for pos in cwr(power_terms, 4):
%o A345148     tot = sum(pos)
%o A345148     keep[tot] += 1
%o A345148 rets = sorted([k for k, v in keep.items() if v >= 6])
%o A345148 for x in range(len(rets)):
%o A345148     print(rets[x])
%Y A345148 Cf. A025371, A343987, A344904, A345083, A345149, A345150, A345174.
%K A345148 nonn
%O A345148 1,1
%A A345148 _David Consiglio, Jr._, Jun 09 2021