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A086668 Number of divisors d of n such that 2d+1 is a prime.

%I A086668 #20 Jun 15 2018 09:25:35
%S A086668 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 A086668 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 A086668 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 A086668 Number of divisors d of n such that 2d+1 is a prime.
%C A086668 From _Antti Karttunen_, Jun 15 2018: (Start)
%C A086668 Number of terms of A005097 that divide n.
%C A086668 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 A086668 (End)
%H A086668 Antti Karttunen, <a href="/A086668/b086668.txt">Table of n, a(n) for n = 1..65537</a>
%F A086668 From _Antti Karttunen_, Jun 15 2018: (Start)
%F A086668 a(n) = Sum_{d|n} A101264(d).
%F A086668 a(n) = A305818(n) + A101264(n).
%F A086668 (End)
%e A086668 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 A086668 Table[Count[Divisors[n],_?(PrimeQ[2#+1]&)],{n,100}] (* _Harvey P. Dale_, Apr 29 2015 *)
%o A086668 (PARI) for (n=2,100,s=0; fordiv(i=n,i,s+=isprime(2*i+1)); print1(","s))
%o A086668 (PARI) A086668(n) = sumdiv(n,d,isprime(d+d+1)); \\ _Antti Karttunen_, Jun 15 2018
%Y A086668 One less than A046886.
%Y A086668 Cf. A005097, A005384, A101264, A305818.
%K A086668 nonn
%O A086668 1,2
%A A086668 _Jon Perry_, Jul 27 2003
%E A086668 Definition modified by _Harvey P. Dale_, Apr 29 2015