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A295798 a(n) is the number of divisors d of prime(n)^2 - 1 such that prime(n) + d is prime. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

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

EXAMPLE

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.

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 *)

PROG

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

CROSSREFS

Cf. A000040, A143958.

Sequence in context: A019759 A019965 A053148 * A072728 A158185 A095413

Adjacent sequences:  A295795 A295796 A295797 * A295799 A295800 A295801

KEYWORD

nonn

AUTHOR

Robert Israel, Nov 27 2017

STATUS

approved

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Last modified August 13 08:18 EDT 2022. Contains 356079 sequences. (Running on oeis4.)