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A345153 Numbers that are the sum of four third powers in exactly eight ways.

%I A345153 #7 Jul 31 2021 23:29:10
%S A345153 27720,30429,31339,31402,33579,34624,34776,36162,40105,42695,44037,
%T A345153 44163,44226,44947,45162,45675,46277,46900,47600,49042,50112,50689,
%U A345153 51058,51597,51805,52227,52264,52507,53144,54271,54873,55692,55790,56240,58032,58221,58312
%N A345153 Numbers that are the sum of four third powers in exactly eight ways.
%C A345153 Differs from A345152 at term 1 because 21896 = 1^3 + 11^3 + 19^3 + 22^3  = 2^3 + 2^3 + 12^3 + 26^3  = 2^3 + 3^3 + 19^3 + 23^3  = 2^3 + 5^3 + 15^3 + 25^3  = 3^3 + 10^3 + 16^3 + 24^3  = 3^3 + 17^3 + 19^3 + 19^3  = 4^3 + 6^3 + 20^3 + 22^3  = 5^3 + 8^3 + 14^3 + 25^3  = 7^3 + 11^3 + 17^3 + 23^3  = 8^3 + 9^3 + 19^3 + 22^3.
%H A345153 David Consiglio, Jr., <a href="/A345153/b345153.txt">Table of n, a(n) for n = 1..10000</a>
%e A345153 30429 is a term because 30429 = 1^3 + 4^3 + 7^3 + 30^3  = 1^3 + 16^3 + 17^3 + 26^3  = 2^3 + 12^3 + 21^3 + 25^3  = 3^3 + 3^3 + 14^3 + 29^3  = 4^3 + 17^3 + 21^3 + 23^3  = 5^3 + 11^3 + 15^3 + 28^3  = 6^3 + 6^3 + 22^3 + 25^3  = 7^3 + 14^3 + 18^3 + 26^3.
%o A345153 (Python)
%o A345153 from itertools import combinations_with_replacement as cwr
%o A345153 from collections import defaultdict
%o A345153 keep = defaultdict(lambda: 0)
%o A345153 power_terms = [x**3 for x in range(1, 1000)]
%o A345153 for pos in cwr(power_terms, 4):
%o A345153     tot = sum(pos)
%o A345153     keep[tot] += 1
%o A345153 rets = sorted([k for k, v in keep.items() if v == 8])
%o A345153 for x in range(len(rets)):
%o A345153     print(rets[x])
%Y A345153 Cf. A025364, A344925, A345088, A345151, A345152, A345154, A345184.
%K A345153 nonn
%O A345153 1,1
%A A345153 _David Consiglio, Jr._, Jun 09 2021