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A345121 Numbers that are the sum of three third powers in ten or more ways.

%I A345121 #7 Aug 05 2021 15:29:30
%S A345121 34012224,58995000,69190848,71319312,72505152,92853216,94118760,
%T A345121 95331816,119095488,119409984,139755888,147545280,150506000,150547032,
%U A345121 157464000,159874560,161023680,161350272,164186352,171904032,175986000,176175000,182393856,184909824
%N A345121 Numbers that are the sum of three third powers in ten or more ways.
%H A345121 Sean A. Irvine, <a href="/A345121/b345121.txt">Table of n, a(n) for n = 1..3429</a>
%e A345121 34012224 is a term 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.
%o A345121 (Python)
%o A345121 from itertools import combinations_with_replacement as cwr
%o A345121 from collections import defaultdict
%o A345121 keep = defaultdict(lambda: 0)
%o A345121 power_terms = [x**3 for x in range(1, 1000)]
%o A345121 for pos in cwr(power_terms, 3):
%o A345121     tot = sum(pos)
%o A345121     keep[tot] += 1
%o A345121 rets = sorted([k for k, v in keep.items() if v >= 10])
%o A345121 for x in range(len(rets)):
%o A345121     print(rets[x])
%Y A345121 Cf. A025338, A344862, A345119, A345122, A345155.
%K A345121 nonn
%O A345121 1,1
%A A345121 _David Consiglio, Jr._, Jun 08 2021
%E A345121 More terms from _Sean A. Irvine_, Jun 08 2021