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A343989 Numbers that are the sum of five positive cubes in five or more ways.

%I A343989 #14 May 10 2024 02:20:49
%S A343989 1765,1980,2043,2104,2195,2250,2430,2449,2486,2491,2493,2547,2584,
%T A343989 2592,2738,2745,2764,2817,2888,2915,2953,2969,2979,3095,3096,3133,
%U A343989 3142,3186,3188,3214,3240,3249,3275,3277,3310,3312,3366,3403,3422,3459,3464,3466,3483,3492,3520,3529,3583,3608,3627,3653,3664,3671
%N A343989 Numbers that are the sum of five positive cubes in five or more ways.
%H A343989 David Consiglio, Jr., <a href="/A343989/b343989.txt">Table of n, a(n) for n = 1..20000</a>
%e A343989 2043 = 1^3 + 4^3 + 5^3 +  5^3 + 12^3
%e A343989      = 2^3 + 2^3 + 3^3 + 10^3 + 10^3
%e A343989      = 2^3 + 3^3 + 4^3 +  6^3 + 12^3
%e A343989      = 4^3 + 5^3 + 5^3 +  9^3 + 10^3
%e A343989      = 4^3 + 6^3 + 6^3 +  6^3 + 11^3
%e A343989 so 2043 is a term.
%o A343989 (Python)
%o A343989 from itertools import combinations_with_replacement as cwr
%o A343989 from collections import defaultdict
%o A343989 keep = defaultdict(lambda: 0)
%o A343989 power_terms = [x**3 for x in range(1,50)]
%o A343989 for pos in cwr(power_terms,5):
%o A343989     tot = sum(pos)
%o A343989     keep[tot] += 1
%o A343989 rets = sorted([k for k,v in keep.items() if v >= 5])
%o A343989 for x in range(len(rets)):
%o A343989     print(rets[x])
%Y A343989 Cf. A343987, A343988, A344034, A344358, A344798, A345174, A345514.
%K A343989 nonn
%O A343989 1,1
%A A343989 _David Consiglio, Jr._, May 06 2021