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A345154 Numbers that are the sum of four third powers in exactly nine ways.

%I A345154 #6 Jul 31 2021 23:29:15
%S A345154 42120,46683,50806,50904,51408,51480,51688,52208,53865,54971,56385,
%T A345154 57113,60515,60984,62433,65303,66276,66339,66430,67158,69048,69832,
%U A345154 69930,71162,72072,72520,72576,72800,73017,77714,77903,79345,79667,79849,80066,80073,81207
%N A345154 Numbers that are the sum of four third powers in exactly nine ways.
%C A345154 Differs from A345146 at term 1 because 21896 = 1^3 + 11^3 + 19^3 + 22^3  = 2^3 + 2^3 + 12^3 + 26^3  = 2^3 + 3^3 + 19^3 + 23^3  = 2^3 + 5^3 + 15^3 + 25^3  = 3^3 + 10^3 + 16^3 + 24^3  = 3^3 + 17^3 + 19^3 + 19^3  = 4^3 + 6^3 + 20^3 + 22^3  = 5^3 + 8^3 + 14^3 + 25^3  = 7^3 + 11^3 + 17^3 + 23^3  = 8^3 + 9^3 + 19^3 + 22^3.
%H A345154 David Consiglio, Jr., <a href="/A345154/b345154.txt">Table of n, a(n) for n = 1..10000</a>
%e A345154 42120 is a term because 42120 = 1^3 + 19^3 + 22^3 + 27^3  = 2^3 + 3^3 + 13^3 + 33^3  = 2^3 + 6^3 + 17^3 + 32^3  = 3^3 + 3^3 + 20^3 + 31^3  = 3^3 + 17^3 + 20^3 + 29^3  = 3^3 + 13^3 + 14^3 + 32^3  = 6^3 + 15^3 + 16^3 + 31^3  = 7^3 + 17^3 + 23^3 + 27^3  = 11^3 + 13^3 + 21^3 + 29^3.
%o A345154 (Python)
%o A345154 from itertools import combinations_with_replacement as cwr
%o A345154 from collections import defaultdict
%o A345154 keep = defaultdict(lambda: 0)
%o A345154 power_terms = [x**3 for x in range(1, 1000)]
%o A345154 for pos in cwr(power_terms, 4):
%o A345154     tot = sum(pos)
%o A345154     keep[tot] += 1
%o A345154 rets = sorted([k for k, v in keep.items() if v == 9])
%o A345154 for x in range(len(rets)):
%o A345154     print(rets[x])
%Y A345154 Cf. A025365, A344927, A345120, A345146, A345153, A345156, A345186.
%K A345154 nonn
%O A345154 1,1
%A A345154 _David Consiglio, Jr._, Jun 09 2021