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A345119 Numbers that are the sum of three third powers in nine or more ways.

%I A345119 #7 Aug 05 2021 15:29:25
%S A345119 14926248,16819704,20168784,34012224,44946000,45580536,54042624,
%T A345119 58995000,59768064,62099136,66203136,67956624,69190848,69393024,
%U A345119 71319312,72505152,78008832,78716448,79539832,80621568,80996544,89354448,90757584,92853216,94118760,95331816
%N A345119 Numbers that are the sum of three third powers in nine or more ways.
%H A345119 David Consiglio, Jr., <a href="/A345119/b345119.txt">Table of n, a(n) for n = 1..37</a>
%e A345119 14926248 is a term because 14926248 = 2^3 + 33^3 + 245^3  = 11^3 + 185^3 + 203^3  = 14^3 + 32^3 + 245^3  = 50^3 + 113^3 + 236^3  = 71^3 + 89^3 + 239^3  = 74^3 + 189^3 + 196^3  = 89^3 + 185^3 + 197^3  = 98^3 + 148^3 + 219^3  = 105^3 + 149^3 + 217^3.
%o A345119 (Python)
%o A345119 from itertools import combinations_with_replacement as cwr
%o A345119 from collections import defaultdict
%o A345119 keep = defaultdict(lambda: 0)
%o A345119 power_terms = [x**3 for x in range(1, 1000)]
%o A345119 for pos in cwr(power_terms, 3):
%o A345119     tot = sum(pos)
%o A345119     keep[tot] += 1
%o A345119 rets = sorted([k for k, v in keep.items() if v >= 9])
%o A345119 for x in range(len(rets)):
%o A345119     print(rets[x])
%Y A345119 Cf. A025337, A344750, A345087, A345120, A345121, A345146.
%K A345119 nonn
%O A345119 1,1
%A A345119 _David Consiglio, Jr._, Jun 08 2021