A343986 - OEIS

%I #11 Jul 31 2021 23:28:59

%S 5105,5131,5616,5859,6435,7777,9315,9737,9793,10017,10250,10458,10936,

%T 10962,11000,11060,11088,11592,11664,11781,12168,12229,12285,12320,

%U 12385,12392,12707,13384,13734,13832,13904,14183,14239,14833,15176,15596,15624,15752,15759,15778,16093,16289,16354,16480,16569

%N Numbers that are the sum of four positive cubes in exactly five ways

%C 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 David Consiglio, Jr., <a href="/A343986/b343986.txt">Table of n, a(n) for n = 1..20000</a>

%e 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 (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**3 for x in range(1,50)]

%o for pos in cwr(power_terms,4):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o rets = sorted([k for k,v in keep.items() if v == 5])

%o for x in range(len(rets)):

%o     print(rets[x])

%Y Cf. A025361, A343970, A343972, A343987, A343988, A344357, A345149.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, May 06 2021