A222563 Primes p such that the sum of divisors (excluding 1 and p - 1) of p - 1 and the sum of divisors (excluding 1 and p + 1) of p + 1 are both prime.

5, 59, 83, 239, 281, 359, 443, 479, 521, 599, 761, 839, 1163, 1319, 1361, 1583, 1619, 1721, 1787, 1871, 1877, 2003, 2063, 2339, 2927, 2969, 3251, 3371, 3407, 3671, 3767, 3917, 4001, 4013, 4229, 4283, 4397, 4451, 4463, 4649, 4679, 5147, 5261, 6287, 6329, 6659, 6689

Offset: 1

Author

Gerasimov Sergey, Feb 25 2013

Keywords

• nonn

Examples

			83 is in the sequence because: it is prime, the sum of divisors (excluding 1 and 82) of 82 is 2 + 41 = 43, which is prime, and the sum of divisors (excluding 1 and 84) of 84 is 2 + 3 + 4 + 6 + 7 + 12 + 14 + 21 + 28 + 42 = 139, which is also prime.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A048050, A085842.

Programs

Mathematica

Select[Prime[Range[2,900]],AllTrue[{Total[Most[Rest[Divisors[#-1]]]], Total[ Most[Rest[Divisors[#+1]]]]},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 29 2016 *)

PARI

is(n)=isprime(n)&&isprime(sigma(n-1)-n)&&isprime(sigma(n+1)-n-2) \\ Charles R Greathouse IV, Feb 25 2013

Extensions

Extended and a(4) and a(6) inserted by Charles R Greathouse IV, Feb 25 2013