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

1,1

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A048050, A085842.

Sequence in context: A096476 A158694 A015994 * A141951 A243701 A179028

Adjacent sequences: A222560 A222561 A222562 * A222564 A222565 A222566

Keyword

nonn

Author

Gerasimov Sergey, Feb 25 2013

Extensions

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

Status

approved