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A345544 Numbers that are the sum of nine cubes in five or more ways.

%I A345544 #6 Aug 05 2021 15:19:10
%S A345544 409,413,428,435,439,446,465,472,479,491,498,502,505,507,512,517,524,
%T A345544 526,531,533,535,538,540,559,561,563,566,568,570,576,579,580,587,594,
%U A345544 596,598,600,601,603,605,613,615,617,620,622,624,627,629,631,632,633,635
%N A345544 Numbers that are the sum of nine cubes in five or more ways.
%H A345544 Sean A. Irvine, <a href="/A345544/b345544.txt">Table of n, a(n) for n = 1..10000</a>
%e A345544 413 is a term because 413 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 5^3 = 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 = 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3 = 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 5^3.
%o A345544 (Python)
%o A345544 from itertools import combinations_with_replacement as cwr
%o A345544 from collections import defaultdict
%o A345544 keep = defaultdict(lambda: 0)
%o A345544 power_terms = [x**3 for x in range(1, 1000)]
%o A345544 for pos in cwr(power_terms, 9):
%o A345544     tot = sum(pos)
%o A345544     keep[tot] += 1
%o A345544     rets = sorted([k for k, v in keep.items() if v >= 5])
%o A345544     for x in range(len(rets)):
%o A345544         print(rets[x])
%Y A345544 Cf. A345502, A345535, A345543, A345545, A345553, A345589, A345797.
%K A345544 nonn
%O A345544 1,1
%A A345544 _David Consiglio, Jr._, Jun 20 2021