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A345188 Numbers that are the sum of five third powers in exactly ten ways.

%I A345188 #10 Jul 31 2021 23:16:57
%S A345188 5860,6588,6651,6859,6947,8056,8289,8569,8758,9045,9099,9227,9414,
%T A345188 9612,9829,10009,10277,10485,10522,10529,10800,10963,10970,11008,
%U A345188 11061,11089,11241,11385,11458,11656,11719,11782,11817,11845,11934,11990,12016,12060,12088
%N A345188 Numbers that are the sum of five third powers in exactly ten ways.
%C A345188 Differs from A345187 at term 8 because 8371 = 1^3 + 1^3 + 11^3 + 11^3 + 16^3  = 1^3 + 4^3 + 5^3 + 12^3 + 17^3  = 1^3 + 8^3 + 9^3 + 11^3 + 16^3  = 3^3 + 3^3 + 4^3 + 15^3 + 15^3  = 3^3 + 3^3 + 8^3 + 8^3 + 18^3  = 3^3 + 3^3 + 3^3 + 5^3 + 19^3  = 3^3 + 7^3 + 9^3 + 9^3 + 17^3  = 4^3 + 6^3 + 6^3 + 11^3 + 17^3  = 5^3 + 9^3 + 10^3 + 11^3 + 15^3  = 6^3 + 6^3 + 12^3 + 13^3 + 13^3  = 8^3 + 8^3 + 9^3 + 9^3 + 16^3.
%H A345188 David Consiglio, Jr., <a href="/A345188/b345188.txt">Table of n, a(n) for n = 1..10000</a>
%e A345188 6588 is a term because 6588 = 1^3 + 3^3 + 5^3 + 7^3 + 17^3  = 1^3 + 4^3 + 6^3 + 13^3 + 14^3  = 1^3 + 5^3 + 8^3 + 8^3 + 16^3  = 1^3 + 10^3 + 10^3 + 11^3 + 12^3  = 2^3 + 2^3 + 9^3 + 12^3 + 14^3  = 2^3 + 3^3 + 8^3 + 11^3 + 15^3  = 3^3 + 8^3 + 8^3 + 11^3 + 14^3  = 3^3 + 3^3 + 5^3 + 10^3 + 16^3  = 5^3 + 5^3 + 8^3 + 10^3 + 15^3  = 8^3 + 9^3 + 10^3 + 10^3 + 12^3.
%o A345188 (Python)
%o A345188 from itertools import combinations_with_replacement as cwr
%o A345188 from collections import defaultdict
%o A345188 keep = defaultdict(lambda: 0)
%o A345188 power_terms = [x**3 for x in range(1, 1000)]
%o A345188 for pos in cwr(power_terms, 5):
%o A345188     tot = sum(pos)
%o A345188     keep[tot] += 1
%o A345188 rets = sorted([k for k, v in keep.items() if v == 10])
%o A345188 for x in range(len(rets)):
%o A345188     print(rets[x])
%Y A345188 Cf. A294744, A341898, A345156, A345186, A345187, A345772.
%K A345188 nonn
%O A345188 1,1
%A A345188 _David Consiglio, Jr._, Jun 10 2021