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

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

Author

Jan Koornstra, Feb 19 2019

Keywords

• nonn
• easy

Comments

Maple and Mathematica programs adapted from A085842.

Examples

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

Links

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

Crossrefs

Cf. A085842, A037020, A000203.

Programs

GAP

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

Maple

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;

Mathematica

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 *)

PARI

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