|
%I #50 Apr 30 2019 21:50:06
%S 0,0,0,0,0,1,1,2,1,2,2,3,3,3,2,3,3,2,3,3,4,4,3,2,4,3,3,4,4,3,5,3,5,4,
%T 6,4,7,2,4,4,6,3,5,3,5,5,5,2,7,3,6,4,6,2,7,3,7,4,5,2,7,3,5,4,6,2,9,2,
%U 7,5,7,2,9,3,6,6,7,3,9,2,8,4,5,4,10,3,8,4,7,3,11,4,8,3,6,2
%N Number of partitions of n into 2 distinct prime powers (not including 1).
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = [x^n y^2] Product_{k>=1} (1 + y*x^A246655(k)).
%e a(12) = 3 because we have [9, 3], [8, 4] and [7, 5].
%t Table[Count[IntegerPartitions[n, {2}], _?(And[UnsameQ @@ #, AllTrue[#, PrimePowerQ[#] &]] &)], {n, 0, 95}]
%Y Cf. A000961, A071330, A106244, A117929, A246655, A307726, A307825.
%K nonn
%O 0,8
%A _Ilya Gutkovskiy_, Apr 30 2019
|
