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A345083 Numbers that are the sum of three third powers in six or more ways.

%I A345083 #10 Aug 05 2021 15:29:12
%S A345083 1296378,1371735,1409400,1614185,1824040,1885248,2016496,2101464,
%T A345083 2302028,2305395,2542968,2562624,2851848,2889216,2974392,2988441,
%U A345083 3185792,3380833,3681280,3689496,3706984,3775680,3906657,4109832,4123008,4142683,4422592,4525632,4783680
%N A345083 Numbers that are the sum of three third powers in six or more ways.
%H A345083 David Consiglio, Jr., <a href="/A345083/b345083.txt">Table of n, a(n) for n = 1..1000</a>
%e A345083 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 A345083 (Python)
%o A345083 from itertools import combinations_with_replacement as cwr
%o A345083 from collections import defaultdict
%o A345083 keep = defaultdict(lambda: 0)
%o A345083 power_terms = [x**3 for x in range(1, 1000)]
%o A345083 for pos in cwr(power_terms, 3):
%o A345083     tot = sum(pos)
%o A345083     keep[tot] += 1
%o A345083 rets = sorted([k for k, v in keep.items() if v >= 6])
%o A345083 for x in range(len(rets)):
%o A345083     print(rets[x])
%Y A345083 Cf. A025334, A343967, A344647, A345084, A345086, A345148.
%K A345083 nonn
%O A345083 1,1
%A A345083 _David Consiglio, Jr._, Jun 07 2021