%N Numbers n such that k*n/(k+n) is never prime for all k.
%C If n were an odd number, k*n/(k+n) would never be prime for all k; these are trivial and are not included. See A242932.
%C It is believed that numbers in A016742 (except 4) are members of this sequence.
%e 16*k/(16+k) is an integer for k = 16, 48, 112, and 240. These k-values give the integers 8, 12, 14, and 15, respectively. Since none are prime, 16 is a member of this sequence.
%o (PARI) a(n)=for(k=1,n*(n-1),s=(k*n)/(k+n);if(floor(s)==s,if(ispseudoprime(s),return(k))))
%o n=1;while(n<300,if(a(2*n)==0,print1(2*n,", "));n+=1)
%Y Cf. A242932.
%A _Derek Orr_, May 27 2014