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A345086 Numbers that are the sum of three third powers in seven or more ways.

%I A345086 #16 Jul 29 2023 13:56:06
%S A345086 2016496,2562624,4525632,4783680,5268024,5618250,6366816,6525000,
%T A345086 6755328,7374375,7451352,7457120,8275392,9063144,9086104,9931167,
%U A345086 10036872,10266138,10371024,10973880,12002472,12452049,12742920,12983517,13581352,13639816,13641480
%N A345086 Numbers that are the sum of three third powers in seven or more ways.
%H A345086 David Consiglio, Jr., <a href="/A345086/b345086.txt">Table of n, a(n) for n = 1..100</a>
%e A345086 2016496 is a term 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.
%o A345086 (Python)
%o A345086 from itertools import combinations_with_replacement as cwr
%o A345086 from collections import defaultdict
%o A345086 keep = defaultdict(lambda: 0)
%o A345086 power_terms = [x**3 for x in range(1, 1000)]
%o A345086 for pos in cwr(power_terms, 3):
%o A345086     tot = sum(pos)
%o A345086     keep[tot] += 1
%o A345086 rets = sorted([k for k, v in keep.items() if v >= 7])
%o A345086 for x in range(len(rets)):
%o A345086     print(rets[x])
%Y A345086 Cf. A025335, A344729, A345083, A345085, A345087, A345150.
%K A345086 nonn
%O A345086 1,1
%A A345086 _David Consiglio, Jr._, Jun 07 2021