A158458 Numbers k such that k + bigomega(k) is prime.

2, 8, 9, 15, 20, 21, 28, 32, 35, 39, 44, 48, 50, 51, 57, 65, 68, 69, 70, 76, 77, 87, 95, 98, 108, 110, 111, 124, 129, 135, 148, 154, 155, 161, 162, 164, 168, 170, 176, 177, 188, 189, 190, 192, 209, 221, 225, 230, 236, 237, 238, 249, 252, 264, 266, 267, 268, 272, 290

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 19 2009

Keywords

• nonn

Comments

2 is the only prime number in the sequence. - Michel Lagneau, May 17 2010

Examples

			a(2) = 8 = 2*2*2; 8+3 = 11 is prime.
a(3) = 9 = 3*3; 9+2 = 11 is prime.
a(4) = 15 = 3*5; 15+2 = 17 is prime.
		

Links

• Eric Chen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001222.

Cf. A067532, A078762, A068080. - Michel Lagneau, May 17 2010

Programs

Maple

for k from 2 to 400 do if isprime(k+numtheory[bigomega](k)) then printf("%d,",k) ; fi; od: # R. J. Mathar, May 19 2009, May 23 2010

Mathematica

Select[Range[10^3], PrimeQ[ # + Plus @@ Last /@ FactorInteger[ # ]] &] (* Michel Lagneau, May 17 2010 *)
Select[Range[300],PrimeQ[#+PrimeOmega[#]]&] (* Harvey P. Dale, Dec 20 2021 *)

PARI

is(n)=isprime(n+bigomega(n)) \\ Eric Chen, Jun 13 2018

Formula

{k: k+A001222(k) in A000040}.

Extensions

191 replaced with 192 and extended by R. J. Mathar, May 19 2009

Generalized (by inserting a(1)=2) by Michel Lagneau, May 17 2010