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A343969 Numbers that are the sum of three positive cubes in exactly 4 ways.

%I A343969 #14 Jul 31 2021 23:41:28
%S A343969 13896,40041,44946,52200,53136,58995,76168,82278,93339,94184,105552,
%T A343969 110683,111168,112384,112832,113400,143424,149416,149904,167616,
%U A343969 169560,171296,175104,196776,197569,208144,216126,221696,222984,224505,235808,240813,252062,255312,262781,266031,281728,291213
%N A343969 Numbers that are the sum of three positive cubes in exactly 4 ways.
%C A343969 Differs from A343968 at term 20 because 161568 = 2^3 + 16^3 + 54^3 = 9^3 + 15^3 + 54^3 = 17^3 + 39^3 + 46^3 = 18^3 + 19^3 + 53^3 = 26^3 + 36^3 + 46^3.
%H A343969 David Consiglio, Jr., <a href="/A343969/b343969.txt">Table of n, a(n) for n = 1..20000</a>
%e A343969 44946 is a term because 44946 = 7^3 + 12^3 + 35^3 = 9^3 + 17^3 + 34^3 = 11^3 + 24^3 + 31^3 = 16^3 + 17^3 + 33^3.
%o A343969 (Python)
%o A343969 from itertools import combinations_with_replacement as cwr
%o A343969 from collections import defaultdict
%o A343969 keep = defaultdict(lambda: 0)
%o A343969 power_terms = [x**3 for x in range(1,50)]
%o A343969 for pos in cwr(power_terms,3):
%o A343969     tot = sum(pos)
%o A343969     keep[tot] += 1
%o A343969 rets = sorted([k for k,v in keep.items() if v == 4])
%o A343969 for x in range(len(rets)):
%o A343969     print(rets[x])
%Y A343969 Cf. A025324, A025397, A343968, A343970, A343972, A344278, A345865.
%K A343969 nonn
%O A343969 1,1
%A A343969 _David Consiglio, Jr._, May 05 2021