%I
%S 0,0,1,2,0,3,0,1,0,1,0,2,0,2,0,0,0,1,0,1,0,1,0,1,0,0,0,2,0,1,0,1,0,0,
%T 0,2,0,0,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0,2,0,0,0,0,0,1,0,0,
%U 0,1,0,2,0,0,0,0,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0,1
%N Number of solutions for k*n/(k+n) = p for integer k > 0 and prime p.
%C It is unknown whether a(6) = 3 is the highest number in this sequence.
%e 4*k/(4+k) has two solutions: k=4,p=2 and k=12,p=3. Thus a(4) = 2.
%o (PARI) a(n) = {t=0;for(k=1,n*(n1),s=k*n/(k+n);if(floor(s)==s,if(ispseudoprime(s),t+=1)));return(t);}
%o n=1;while(n<100,print1(a(n),", ");n+=1)
%K nonn
%O 1,4
%A _Derek Orr_, May 29 2014
