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A345152 Numbers that are the sum of four third powers in eight or more ways.

%I A345152 #7 Aug 05 2021 15:27:33
%S A345152 21896,27720,30429,31339,31402,33579,34624,34776,36162,36225,40105,
%T A345152 42120,42695,44037,44163,44226,44947,45162,45675,46277,46683,46872,
%U A345152 46900,47600,48321,48825,49042,50112,50689,50806,50904,51058,51408,51480,51506,51597,51688
%N A345152 Numbers that are the sum of four third powers in eight or more ways.
%H A345152 David Consiglio, Jr., <a href="/A345152/b345152.txt">Table of n, a(n) for n = 1..10000</a>
%e A345152 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 A345152 (Python)
%o A345152 from itertools import combinations_with_replacement as cwr
%o A345152 from collections import defaultdict
%o A345152 keep = defaultdict(lambda: 0)
%o A345152 power_terms = [x**3 for x in range(1, 1000)]
%o A345152 for pos in cwr(power_terms, 4):
%o A345152     tot = sum(pos)
%o A345152     keep[tot] += 1
%o A345152 rets = sorted([k for k, v in keep.items() if v >= 8])
%o A345152 for x in range(len(rets)):
%o A345152     print(rets[x])
%Y A345152 Cf. A025373, A344924, A345087, A345146, A345150, A345153, A345183.
%K A345152 nonn
%O A345152 1,1
%A A345152 _David Consiglio, Jr._, Jun 09 2021