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A343968 Numbers that are the sum of three positive cubes in four or more ways.

%I A343968 #17 May 10 2024 02:16:58
%S A343968 13896,40041,44946,52200,53136,58995,76168,82278,93339,94184,105552,
%T A343968 110683,111168,112384,112832,113400,143424,149416,149904,161568,
%U A343968 167616,169560,171296,175104,196776,197569,208144,216126,221696,222984,224505,235808,240813,252062,255312,262683,262781,266031
%N A343968 Numbers that are the sum of three positive cubes in four or more ways.
%H A343968 David Consiglio, Jr., <a href="/A343968/b343968.txt">Table of n, a(n) for n = 1..20000</a>
%e A343968 44946 =  7^3 + 12^3 + 35^3
%e A343968       =  9^3 + 17^3 + 34^3
%e A343968       = 11^3 + 24^3 + 31^3
%e A343968       = 16^3 + 17^3 + 33^3
%e A343968 so 44946 is a term.
%o A343968 (Python)
%o A343968 from itertools import combinations_with_replacement as cwr
%o A343968 from collections import defaultdict
%o A343968 keep = defaultdict(lambda: 0)
%o A343968 power_terms = [x**3 for x in range(1,50)]
%o A343968 for pos in cwr(power_terms,3):
%o A343968     tot = sum(pos)
%o A343968     keep[tot] += 1
%o A343968 rets = sorted([k for k,v in keep.items() if v >= 4])
%o A343968 for x in range(len(rets)):
%o A343968     print(rets[x])
%Y A343968 Cf. A023051, A025332, A025398, A343967, A343969, A343971, A344277.
%K A343968 nonn
%O A343968 1,1
%A A343968 _David Consiglio, Jr._, May 05 2021