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A343967 Numbers that are the sum of three positive cubes in five or more ways.

%I A343967 #17 May 10 2024 02:17:06
%S A343967 161568,262683,314712,326808,359568,443197,444536,471960,503208,
%T A343967 513729,515376,526023,529199,532683,552824,597960,702729,736371,
%U A343967 746992,806688,844416,863379,907479,924048,931419,975213,1011067,1028663,1062937,1092853,1152152,1172016,1211048,1232496,1258011
%N A343967 Numbers that are the sum of three positive cubes in five or more ways.
%H A343967 David Consiglio, Jr., <a href="/A343967/b343967.txt">Table of n, a(n) for n = 1..20000</a>
%e A343967 314712 =  4^3 +  6^3 + 68^3
%e A343967        =  5^3 + 24^3 + 67^3
%e A343967        =  6^3 + 30^3 + 66^3
%e A343967        = 31^3 + 41^3 + 60^3
%e A343967        = 36^3 + 48^3 + 54^3
%e A343967 so 314712 is a term of this sequence.
%o A343967 (Python)
%o A343967 from itertools import combinations_with_replacement as cwr
%o A343967 from collections import defaultdict
%o A343967 keep = defaultdict(lambda: 0)
%o A343967 power_terms = [x**3 for x in range(1,50)]
%o A343967 for pos in cwr(power_terms,3):
%o A343967     tot = sum(pos)
%o A343967     keep[tot] += 1
%o A343967 rets = sorted([k for k,v in keep.items() if v >= 5])
%o A343967 for x in range(len(rets)):
%o A343967     print(rets[x])
%Y A343967 Cf. A025333, A051167, A343968, A343970, A343987, A344364, A345083.
%K A343967 nonn
%O A343967 1,1
%A A343967 _David Consiglio, Jr._, May 05 2021