%I
%S 0,0,1,2,1,4,3,8,5,4,0,12,10,20,11,16,5,28,22,38,18,28,14,48,34,32,7,
%T 24,26,56,30,64,47,68,23,60,34,68,54,58,21,112,85,144,59,104,62,168,
%U 82,124,61,110,83,180,81,124,71,152,62,202,91,192,132,224,74
%N Sum of the differences of the larger and smaller parts in the partitions of n into two parts with the larger part prime and smaller part squarefree.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..floor(n/2)} (n  2i) * A008966(i) * A010051(n  i).
%t Table[Sum[(n  2 i) (PrimePi[n  i]  PrimePi[n  i  1]) MoebiusMu[i]^2, {i, Floor[n/2]}], {n, 80}]
%Y Cf. A010051, A008966, A294095.
%K nonn,easy
%O 1,4
%A _Wesley Ivan Hurt_, Oct 22 2017
