cp's OEIS Frontend

A339615 Number of nonempty sets of distinct positive integers whose sum of cubes is a cube, the largest integer of a set is n.

%I A339615 #15 Dec 11 2020 22:57:11
%S A339615 1,1,1,1,2,1,1,3,1,6,5,9,10,25,32,51,97,144,244,463,767,1062,2005,
%T A339615 4177,5716,12101,21526,35306,64629,114871,205337,372317,718410,
%U A339615 1226320,2361112,4308192,7301384,14615750,26382095,47631200,91388286,171931627,302867194,578843590,1112232587
%N A339615 Number of nonempty sets of distinct positive integers whose sum of cubes is a cube, the largest integer of a set is n.
%e A339615 a(13) = 10 sets: {13}, {2, 3, 8, 13}, {4, 8, 11, 12, 13}, {1, 2, 6, 7, 11, 13}, {2, 5, 7, 8, 12, 13}, {3, 4, 8, 10, 11, 12, 13}, {1, 2, 3, 4, 5, 7, 11, 13}, {2, 3, 4, 6, 7, 8, 9, 13}, {1, 2, 5, 6, 7, 8, 9, 10, 12, 13} and {2, 3, 5, 7, 8, 9, 10, 11, 12, 13}.
%o A339615 (Python)
%o A339615 from functools import lru_cache
%o A339615 def perf_cube(n): return round(n**(1/3))**3 ==n
%o A339615 @lru_cache(maxsize=None)
%o A339615 def b(n, soc, c):
%o A339615   if n == 0:
%o A339615     if perf_cube(soc): return 1
%o A339615     return 0
%o A339615   return b(n-1, soc, c) + b(n-1, soc+n*n*n, c+1)
%o A339615 a = lambda n: b(n-1, n*n*n, 1)
%o A339615 print([a(n) for n in range(1, 21)]) # _Michael S. Branicky_, Dec 10 2020
%Y A339615 Cf. A000578, A126111, A339612.
%K A339615 nonn
%O A339615 1,5
%A A339615 _Ilya Gutkovskiy_, Dec 10 2020
%E A339615 a(24)-a(41) from _Michael S. Branicky_, Dec 10 2020
%E A339615 a(42)-a(45) from _Alois P. Heinz_, Dec 11 2020