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A343986 Numbers that are the sum of four positive cubes in exactly five ways.

%I A343986 #13 Jul 23 2025 16:02:45
%S A343986 5105,5131,5616,5859,6435,7777,9315,9737,9793,10017,10250,10458,10936,
%T A343986 10962,11000,11060,11088,11592,11664,11781,12168,12229,12285,12320,
%U A343986 12385,12392,12707,13384,13734,13832,13904,14183,14239,14833,15176,15596,15624,15752,15759,15778,16093,16289,16354,16480,16569
%N A343986 Numbers that are the sum of four positive cubes in exactly five ways.
%C A343986 Differs from A343987 at term 6 because 6883 = 2^3 + 2^3 + 2^3 + 19^3 = 2^3 + 5^3 + 15^3 + 15^3 = 3^3 + 8^3 + 8^3 + 18^3 = 4^3 + 11^3 + 14^3 + 14^3 = 5^3 + 11^3 + 11^3 + 16^3 = 8^3 + 9^3 + 9^3 + 17^3.
%H A343986 David Consiglio, Jr., <a href="/A343986/b343986.txt">Table of n, a(n) for n = 1..20000</a>
%e A343986 5616 is a term because 5616 = 1^3 + 8^3 + 12^3 + 15^3 = 2^3 + 8^3 + 10^3 + 16^3 = 4^3 + 4^3 + 14^3 + 14^3 = 4^3 + 5^3 + 11^3 + 16^3 = 8^3 + 9^3 + 10^3 + 15^3.
%o A343986 (Python)
%o A343986 from itertools import combinations_with_replacement as cwr
%o A343986 from collections import defaultdict
%o A343986 keep = defaultdict(lambda: 0)
%o A343986 power_terms = [x**3 for x in range(1,50)]
%o A343986 for pos in cwr(power_terms,4):
%o A343986     tot = sum(pos)
%o A343986     keep[tot] += 1
%o A343986 rets = sorted([k for k,v in keep.items() if v == 5])
%o A343986 for x in range(len(rets)):
%o A343986     print(rets[x])
%Y A343986 Cf. A025361, A343970, A343972, A343987, A343988, A344357, A345149.
%K A343986 nonn
%O A343986 1,1
%A A343986 _David Consiglio, Jr._, May 06 2021