A116661 Integers in both sequences A114522 and A063989.

4, 6, 8, 9, 10, 12, 18, 20, 22, 25, 27, 32, 34, 44, 48, 49, 50, 58, 68, 72, 80, 82, 108, 116, 118, 121, 125, 128, 142, 162, 164, 165, 169, 176, 192, 200, 202, 214, 236, 242, 243, 272, 273, 274, 284, 288, 289, 298, 320, 343, 345, 358, 361, 382, 385, 394, 399, 404

Offset: 1

Author

Leroy Quet, Feb 21 2006

Keywords

• nonn

Examples

			20 = 2^2 *5^1. Both the number of prime divisors (counted with multiplicity), 2+1 = 3 and the sum of the distinct prime divisors, 2+5 = 7, are primes. So 20 is in the sequence.
		

Links

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

Crossrefs

Cf. A114522, A063989, A116660.

Programs

Magma

f:=func; [k:k in [2..450]| IsPrime(f(k)) and IsPrime(&+PrimeDivisors(k))]; // Marius A. Burtea, Nov 14 2019

Mathematica

Select[Range[500],AllTrue[{PrimeOmega[#],Total[FactorInteger[#][[All, 1]]]}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 03 2019 *)

Extensions

More terms from Robert Gerbicz, Jun 09 2007