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A345084 Numbers that are the sum of three third powers in exactly six ways.

%I A345084 #8 Jul 31 2021 23:41:34
%S A345084 1296378,1371735,1409400,1614185,1824040,1885248,2101464,2302028,
%T A345084 2305395,2542968,2851848,2889216,2974392,2988441,3185792,3380833,
%U A345084 3681280,3689496,3706984,3775680,3906657,4109832,4123008,4142683,4422592,4842872,4952312,5005125,5023656
%N A345084 Numbers that are the sum of three third powers in exactly six ways.
%C A345084 Differs from A345083 at term 7 because 2016496 = 5^3 + 71^3 + 117^3  = 9^3 + 65^3 + 119^3  = 18^3 + 20^3 + 125^3  = 46^3 + 96^3 + 99^3  = 53^3 + 59^3 + 117^3  = 65^3 + 89^3 + 99^3  = 82^3 + 84^3 + 93^3.
%H A345084 David Consiglio, Jr., <a href="/A345084/b345084.txt">Table of n, a(n) for n = 1..1000</a>
%e A345084 1296378 is a term because 1296378 = 3^3 + 75^3 + 94^3  = 8^3 + 32^3 + 107^3  = 20^3 + 76^3 + 93^3  = 30^3 + 58^3 + 101^3  = 32^3 + 80^3 + 89^3  = 59^3 + 74^3 + 86^3.
%o A345084 (Python)
%o A345084 from itertools import combinations_with_replacement as cwr
%o A345084 from collections import defaultdict
%o A345084 keep = defaultdict(lambda: 0)
%o A345084 power_terms = [x**3 for x in range(1, 1000)]
%o A345084 for pos in cwr(power_terms, 3):
%o A345084     tot = sum(pos)
%o A345084     keep[tot] += 1
%o A345084 rets = sorted([k for k, v in keep.items() if v == 6])
%o A345084 for x in range(len(rets)):
%o A345084     print(rets[x])
%Y A345084 Cf. A025326, A343970, A344648, A345083, A345085, A345149.
%K A345084 nonn
%O A345084 1,1
%A A345084 _David Consiglio, Jr._, Jun 07 2021