A295798 a(n) is the number of divisors d of prime(n)^2 - 1 such that prime(n) + d is prime.

2, 3, 5, 5, 8, 6, 7, 11, 7, 13, 13, 8, 16, 11, 7, 11, 11, 8, 9, 23, 5, 13, 9, 22, 12, 14, 15, 8, 20, 12, 20, 19, 8, 20, 14, 19, 5, 12, 10, 7, 12, 33, 24, 7, 18, 28, 20, 13, 9, 15, 21, 27, 20, 29, 12, 11, 14, 30, 5, 25, 4, 10, 33, 19, 7, 3, 12, 18, 9, 26, 13, 19, 13, 12, 40, 9, 15, 12, 24, 17, 37, 17

Offset: 1

Author

Robert Israel, Nov 27 2017

Keywords

• nonn

Comments

a(n) is the number of semiprimes in A143958 whose least prime factor is prime(n).

The least n for which a(n)=0 is 7511.

Examples

			For n=3, prime(3)=5; 5^2-1 has 5 divisors d such that 5+d is prime, namely 2, 6, 8, 12, 24.  Thus a(3)=5.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A143958.

Programs

Maple

f:= proc(p) nops(select(t -> isprime(p+t), numtheory:-divisors(p^2-1))) end proc:
map(f, [seq(ithprime(i),i=1..100)]);

Mathematica

Table[DivisorSum[p^2 - 1, 1 &, PrimeQ[p + #] &], {p, Prime@ Range@ 82}] (* Michael De Vlieger, Nov 27 2017 *)

PARI

a(n) = sumdiv(prime(n)^2-1, d, isprime(prime(n)+d)); \\ Michel Marcus, Nov 30 2017