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A345120 Numbers that are the sum of three third powers in exactly nine ways.

%I A345120 #10 Jul 31 2021 23:41:44
%S A345120 14926248,16819704,20168784,44946000,45580536,54042624,59768064,
%T A345120 62099136,66203136,67956624,69393024,78008832,78716448,79539832,
%U A345120 80621568,80996544,89354448,90757584,99616392,100088568,101352168,101943360,112216896,112720896,114306984
%N A345120 Numbers that are the sum of three third powers in exactly nine ways.
%C A345120 Differs from A345119 at term 4 because 34012224 = 35^3 + 215^3 + 287^3  = 38^3 + 152^3 + 311^3  = 40^3 + 113^3 + 318^3  = 44^3 + 245^3 + 266^3  = 71^3 + 113^3 + 317^3  = 99^3 + 191^3 + 295^3  = 101^3 + 226^3 + 276^3  = 117^3 + 185^3 + 295^3  = 161^3 + 215^3 + 269^3  = 172^3 + 213^3 + 266^3.
%H A345120 Sean A. Irvine, <a href="/A345120/b345120.txt">Table of n, a(n) for n = 1..6359</a>
%e A345120 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 A345120 (Python)
%o A345120 from itertools import combinations_with_replacement as cwr
%o A345120 from collections import defaultdict
%o A345120 keep = defaultdict(lambda: 0)
%o A345120 power_terms = [x**3 for x in range(1, 1000)]
%o A345120 for pos in cwr(power_terms, 3):
%o A345120     tot = sum(pos)
%o A345120     keep[tot] += 1
%o A345120 rets = sorted([k for k, v in keep.items() if v == 9])
%o A345120 for x in range(len(rets)):
%o A345120     print(rets[x])
%Y A345120 Cf. A025329, A344751, A345088, A345119, A345122, A345154.
%K A345120 nonn
%O A345120 1,1
%A A345120 _David Consiglio, Jr._, Jun 08 2021