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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000203, A056798.

Sequence in context: A139522 A163158 A355981 * A112089 A075062 A022497

Adjacent sequences: A171127 A171128 A171129 * A171131 A171132 A171133

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 04 2009

Extensions

More terms from Michel Marcus, Sep 30 2014

Status

approved