A085842 -id:A085842 - cp's OEIS frontend

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

Gerasimov Sergey, Feb 25 2013

nonn

			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.

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

Cf. A048050, A085842.

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 *)

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

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

A306490 Numbers k such that sigma(k) - k - 2 is prime.

Original entry on oeis.org

8, 9, 15, 16, 18, 27, 32, 33, 35, 36, 45, 50, 51, 64, 65, 75, 77, 87, 91, 95, 98, 119, 123, 125, 135, 143, 144, 147, 153, 161, 162, 175, 177, 185, 195, 200, 207, 209, 213, 215, 217, 221, 231, 247, 259, 261, 273, 285, 287, 297, 303, 315, 321

Offset: 1

Jan Koornstra, Feb 19 2019

Maple and Mathematica programs adapted from A085842.

			The divisors of 8 are {1, 2, 4, 8}. sigma(8) - 8 - 2 = 5, which is prime.

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

Cf. A085842, A037020, A000203.

Filtered([2..330],k->IsPrime(Sigma(k)-k-2)); # Muniru A Asiru, Feb 24 2019

with(numtheory): b := []: for n from 3 to 2000 do t1 := divisors(n); t2 := convert(t1, list); t3 := add(t2[i], i=1..nops(t2)); if isprime(t3-2-n) then b := [op(b), n]; fi; od: b;

f[n_]:=Plus@@Divisors[n]-n-2; lst={}; Do[a=f[n]; If[PrimeQ[a], AppendTo[lst, n]], {n, 7!}]; lst
Select[Range[2, 500], PrimeQ[DivisorSigma[1, #] - # - 2] &] (* Vaclav Kotesovec, Feb 23 2019 *)

isok(n) = isprime(sigma(n) - n - 2); \\ Michel Marcus, Feb 23 2019

cp's OEIS Frontend

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.

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