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A343987 Numbers that are the sum of four positive cubes in five or more ways.

%I A343987 #19 May 10 2024 02:16:37
%S A343987 5105,5131,5616,5859,6435,6883,7777,9315,9737,9793,10017,10250,10458,
%T A343987 10936,10962,11000,11060,11088,11592,11664,11781,12168,12229,12285,
%U A343987 12320,12385,12392,12411,12707,13104,13384,13734,13832,13904,13923,14112,14183,14239,14581,14833,14896,14904,15176,15561,15596
%N A343987 Numbers that are the sum of four positive cubes in five or more ways.
%H A343987 David Consiglio, Jr., <a href="/A343987/b343987.txt">Table of n, a(n) for n = 1..20000</a>
%e A343987 5616 = 1^3 + 8^3 + 12^3 + 15^3
%e A343987      = 2^3 + 8^3 + 10^3 + 16^3
%e A343987      = 4^3 + 4^3 + 14^3 + 14^3
%e A343987      = 4^3 + 5^3 + 11^3 + 16^3
%e A343987      = 8^3 + 9^3 + 10^3 + 15^3
%e A343987 so 5616 is a term.
%o A343987 (Python)
%o A343987 from itertools import combinations_with_replacement as cwr
%o A343987 from collections import defaultdict
%o A343987 keep = defaultdict(lambda: 0)
%o A343987 power_terms = [x ** 3 for x in range(1, 50)]
%o A343987 for pos in cwr(power_terms, 4):
%o A343987     tot = sum(pos)
%o A343987     keep[tot] += 1
%o A343987 rets = sorted([k for k, v in keep.items() if v >= 5])
%o A343987 for x in range(len(rets)):
%o A343987     print(rets[x], end=", ")
%Y A343987 Cf. A025370, A343967, A343971, A343986, A343989, A344356, A345148.
%K A343987 nonn
%O A343987 1,1
%A A343987 _David Consiglio, Jr._, May 06 2021