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A131799 Number of partitions of n into parts that are squares or cubes.

%I A131799 #26 Aug 01 2020 12:02:36
%S A131799 1,1,1,1,2,2,2,2,4,5,5,5,7,8,8,8,12,14,15,15,19,21,22,22,28,33,35,37,
%T A131799 43,48,50,52,61,69,74,78,90,98,103,107,122,135,143,152,170,186,194,
%U A131799 203,225,247,261,275,305,330,348,362,396,429,454,477,519,561,590,618,666,717
%N A131799 Number of partitions of n into parts that are squares or cubes.
%C A131799 a(n) = A078635(n) for n < 32 = 2^5.
%H A131799 Vaclav Kotesovec, <a href="/A131799/b131799.txt">Table of n, a(n) for n = 0..1000</a>
%F A131799 G.f.: Product_{k>=1} (1 - x^(k^6)) / ((1 - x^(k^2)) * (1 - x^(k^3))). - _Vaclav Kotesovec_, Jan 12 2017
%e A131799 a(10) = #{9+1, 8+1+1, 4+4+1+1, 4+1+1+1+1+1+1, 1+1+1+1+1+1+1+1+1+1} = 5.
%t A131799 nmax = 65; c2max = nmax^(1/2); c3max = nmax^(1/3);
%t A131799 s = Flatten[{Table[n^2, {n, 1, c2max}]}~Join~{Table[n^3, {n, 1, c3max}]}];
%t A131799 Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 0, nmax}] (* _Robert Price_, Jul 31 2020 *)
%Y A131799 Cf. A000041, A001156, A002760, A003108, A078635.
%K A131799 nonn
%O A131799 0,5
%A A131799 _Reinhard Zumkeller_, Jul 16 2007
%E A131799 a(0)=1 prepended by _Ilya Gutkovskiy_, Jan 11 2017