A345542 - OEIS

%I #8 Jan 04 2022 15:14:28

%S 224,231,238,245,250,257,259,264,271,276,278,280,283,285,287,290,292,

%T 294,297,299,301,302,309,311,313,315,316,318,320,322,327,334,335,337,

%U 339,341,346,348,350,353,355,357,362,365,372,374,376,379,381,383,386,387

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

%H Sean A. Irvine, <a href="/A345542/b345542.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 Select[Range[400],Length[Select[PowersRepresentations[#,9,3],FreeQ[ #,0]&]]> 2&] (* _Harvey P. Dale_, Jan 04 2022 *)

%o (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**3 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 9):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o     rets = sorted([k for k, v in keep.items() if v >= 3])

%o     for x in range(len(rets)):

%o         print(rets[x])

%Y Cf. A345500, A345533, A345541, A345543, A345551, A345587, A345795.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 20 2021

%E Definition corrected by _Harvey P. Dale_, Jan 04 2022