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A343971 Numbers that are the sum of four positive cubes in four or more ways.

%I A343971 #16 May 10 2024 02:16:48
%S A343971 1979,2737,3663,4384,4445,4474,4949,5105,5131,5257,5320,5473,5499,
%T A343971 5553,5616,5733,5768,5833,5852,5859,6064,6104,6328,6372,6435,6587,
%U A343971 6643,6832,6883,6912,6974,7000,7030,7120,7217,7371,7560,7686,7777,7840,8099,8108,8281,8316,8344,8379,8414,8505,8568,8927,9016,9018
%N A343971 Numbers that are the sum of four positive cubes in four or more ways.
%H A343971 David Consiglio, Jr., <a href="/A343971/b343971.txt">Table of n, a(n) for n = 1..20000</a>
%e A343971 3663 = 1^3 + 10^3 + 11^3 + 11^3
%e A343971      = 2^3 +  4^3 +  6^3 + 15^3
%e A343971      = 2^3 +  9^3 +  9^3 + 13^3
%e A343971      = 4^3 +  7^3 +  8^3 + 14^3
%e A343971 so 3663 is a term.
%o A343971 (Python)
%o A343971 from itertools import combinations_with_replacement as cwr
%o A343971 from collections import defaultdict
%o A343971 keep = defaultdict(lambda: 0)
%o A343971 power_terms = [x**3 for x in range(1,50)]
%o A343971 for pos in cwr(power_terms,4):
%o A343971     tot = sum(pos)
%o A343971     keep[tot] += 1
%o A343971 rets = sorted([k for k,v in keep.items() if v >= 4])
%o A343971 for x in range(len(rets)):
%o A343971     print(rets[x])
%Y A343971 Cf. A025369, A025407, A343968, A343972, A343987, A344034, A344352.
%K A343971 nonn
%O A343971 1,1
%A A343971 _David Consiglio, Jr._, May 05 2021