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%I #20 Jun 15 2018 09:25:35
%S 1,2,2,2,2,4,1,3,3,3,2,4,1,3,4,3,1,6,1,4,3,3,2,5,2,3,3,3,2,7,1,3,4,2,
%T 3,7,1,2,3,5,2,6,1,4,5,3,1,6,1,4,3,3,2,7,3,5,2,3,1,8,1,2,5,3,3,6,1,3,
%U 4,5,1,8,1,3,5,2,2,7,1,5,4,3,2,6,2,3,3,5,2,10,1,3,2,2,3,7,1,4,6,5
%N Number of divisors d of n such that 2d+1 is a prime.
%C From _Antti Karttunen_, Jun 15 2018: (Start)
%C Number of terms of A005097 that divide n.
%C For all n >= 1, a(n) > A156660(n). Specifically, a(p) = 2 for all p in A005384 (Sophie Germain primes), although 2's occur in other positions as well.
%C (End)
%H Antti Karttunen, <a href="/A086668/b086668.txt">Table of n, a(n) for n = 1..65537</a>
%F From _Antti Karttunen_, Jun 15 2018: (Start)
%F a(n) = Sum_{d|n} A101264(d).
%F a(n) = A305818(n) + A101264(n).
%F (End)
%e 10 has divisors 1,2,5 and 10 of which 2.1+1, 2.2+1 and 2.5+1 are prime, so a(10)=3
%t Table[Count[Divisors[n],_?(PrimeQ[2#+1]&)],{n,100}] (* _Harvey P. Dale_, Apr 29 2015 *)
%o (PARI) for (n=2,100,s=0; fordiv(i=n,i,s+=isprime(2*i+1)); print1(","s))
%o (PARI) A086668(n) = sumdiv(n,d,isprime(d+d+1)); \\ _Antti Karttunen_, Jun 15 2018
%Y One less than A046886.
%Y Cf. A005097, A005384, A101264, A305818.
%K nonn
%O 1,2
%A _Jon Perry_, Jul 27 2003
%E Definition modified by _Harvey P. Dale_, Apr 29 2015
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