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A343972 Numbers that are the sum of four positive cubes in exactly four ways.

%I A343972 #11 Jul 31 2021 23:28:56
%S A343972 1979,2737,3663,4384,4445,4474,4949,5257,5320,5473,5499,5553,5733,
%T A343972 5768,5833,5852,6064,6104,6328,6372,6587,6643,6832,6912,6974,7000,
%U A343972 7030,7120,7217,7371,7560,7686,7840,8099,8108,8281,8316,8344,8379,8414,8505,8568,8927,9016,9018,9044,9072,9100,9289,9548,9648,9800
%N A343972 Numbers that are the sum of four positive cubes in exactly four ways.
%C A343972 This sequence varies from A343971 at term 8 because 5105 = 1^3 + 1^3 + 12^3 + 15^3 = 1^3 + 2^3 + 10^3 + 16^3 = 1^3 + 9^3 + 10^3 + 15^3 = 4^3 + 4^3 + 4^3 + 17^3 = 4^3 + 6^3 + 9^3 + 16^3.
%H A343972 David Consiglio, Jr., <a href="/A343972/b343972.txt">Table of n, a(n) for n = 1..20000</a>
%e A343972 3663 is a term because 3663 = 1^3 + 10^3 + 11^3 + 11^3 = 2^3 + 4^3 + 6^3 + 15^3 = 2^3 + 9^3 + 9^3 + 13^3 = 4^3 + 7^3 + 8^3 + 14^3.
%o A343972 (Python)
%o A343972 from itertools import combinations_with_replacement as cwr
%o A343972 from collections import defaultdict
%o A343972 keep = defaultdict(lambda: 0)
%o A343972 power_terms = [x**3 for x in range(1,50)]
%o A343972 for pos in cwr(power_terms,4):
%o A343972     tot = sum(pos)
%o A343972     keep[tot] += 1
%o A343972 rets = sorted([k for k,v in keep.items() if v == 4])
%o A343972 for x in range(len(rets)):
%o A343972     print(rets[x])
%Y A343972 Cf. A025360, A025405, A343969, A343971, A343986, A344035, A344353.
%K A343972 nonn
%O A343972 1,1
%A A343972 _David Consiglio, Jr._, May 05 2021