A171130 Primes p such that sum of divisors of p+2 is prime.

2, 7, 23, 727, 2399, 5039, 7919, 17159, 28559, 29927, 85847, 458327, 552047, 579119, 707279, 1190279, 3418799, 3728759, 4532639, 5166527, 5331479, 7447439, 10374839, 24137567, 25877567, 28398239, 30260999, 43546799, 47458319, 52258439, 56957207, 62425799

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 04 2009

Keywords

• nonn

Comments

If p is a term then p+2 is a prime power with an even exponent (A056798). - Amiram Eldar, Aug 01 2024

Examples

			2 is a term since it is a prime and sigma(2+2) = 7 is a prime.
7 is a term since it is a prime and sigma(7+2) = 13 is a prime.
23 is a term since it is a prime and sigma(23+2) = 31 is a prime.
727 is a term since it is a prime and sigma(727+2) = 1093 is a prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A056798.

Programs

Maple

with(numtheory): A171130:=n->`if`(isprime(n) and isprime(sigma(n+2)), n, NULL): seq(A171130(n), n=1..10^5); # Wesley Ivan Hurt, Sep 30 2014

Mathematica

f[n_]:=Plus@@Divisors[n]; lst={};Do[p=Prime[n];If[PrimeQ[f[p+2]],AppendTo[lst,p]],{n,10!}];lst
Select[Prime[Range[700000]],PrimeQ[DivisorSigma[1,#+2]]&] (* Harvey P. Dale, Jun 23 2011 *)

PARI

lista(nn) = forprime(p=2, nn, if (isprime(sigma(p+2)), print1(p, ", "))); \\ Michel Marcus, Sep 30 2014

PARI

lista(kmax) = {my(p); for(k = 1, kmax, if(isprime(k) || isprimepower(k), p = k^2-2; if(isprime(p) && isprime(sigma(p+2)), print1(p, ", "))));} \\ Amiram Eldar, Aug 01 2024

Extensions

More terms from Michel Marcus, Sep 30 2014