I've been considering a twinprime analogy to the sum
sum (n<=x) M(n)/n = log x+O(1)
where M(n) is the Mangoldt function. My formula is this:
f(x)=sum (2<n<=x, condition M(n)*M(n+2)<>0) M(n)/n = 2*H*loglog x
where H is the twinprime constant=0.66016...
so that f(20)=log (3)/3+log(5)/5+log(7)/7+log(3)/9+log(11)/11+log
(17)/17=1.472797 and for each added term in the sum it adds
according to where the powers of prime pairs exist.
I've tested this function for all x less than half a million, and it