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A345542 Numbers that are the sum of nine positive cubes in three or more ways.

%I A345542 #8 Jan 04 2022 15:14:28
%S A345542 224,231,238,245,250,257,259,264,271,276,278,280,283,285,287,290,292,
%T A345542 294,297,299,301,302,309,311,313,315,316,318,320,322,327,334,335,337,
%U A345542 339,341,346,348,350,353,355,357,362,365,372,374,376,379,381,383,386,387
%N A345542 Numbers that are the sum of nine positive cubes in three or more ways.
%H A345542 Sean A. Irvine, <a href="/A345542/b345542.txt">Table of n, a(n) for n = 1..10000</a>
%e A345542 231 is a term because 231 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 5^3 = 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3.
%t A345542 Select[Range[400],Length[Select[PowersRepresentations[#,9,3],FreeQ[ #,0]&]]> 2&] (* _Harvey P. Dale_, Jan 04 2022 *)
%o A345542 (Python)
%o A345542 from itertools import combinations_with_replacement as cwr
%o A345542 from collections import defaultdict
%o A345542 keep = defaultdict(lambda: 0)
%o A345542 power_terms = [x**3 for x in range(1, 1000)]
%o A345542 for pos in cwr(power_terms, 9):
%o A345542     tot = sum(pos)
%o A345542     keep[tot] += 1
%o A345542     rets = sorted([k for k, v in keep.items() if v >= 3])
%o A345542     for x in range(len(rets)):
%o A345542         print(rets[x])
%Y A345542 Cf. A345500, A345533, A345541, A345543, A345551, A345587, A345795.
%K A345542 nonn
%O A345542 1,1
%A A345542 _David Consiglio, Jr._, Jun 20 2021
%E A345542 Definition corrected by _Harvey P. Dale_, Jan 04 2022