A295798 - OEIS

%I #16 Nov 30 2017 04:05:40

%S 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,

%T 20,12,20,19,8,20,14,19,5,12,10,7,12,33,24,7,18,28,20,13,9,15,21,27,

%U 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

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

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

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

%H Robert Israel, <a href="/A295798/b295798.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p f:= proc(p) nops(select(t -> isprime(p+t), numtheory:-divisors(p^2-1))) end proc:

%p map(f, [seq(ithprime(i),i=1..100)]);

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

%o (PARI) a(n) = sumdiv(prime(n)^2-1, d, isprime(prime(n)+d)); \\ _Michel Marcus_, Nov 30 2017

%Y Cf. A000040, A143958.

%K nonn

%O 1,1

%A _Robert Israel_, Nov 27 2017