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

1,1

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A114522, A063989, A116660.

Sequence in context: A248807 A034878 A173328 * A109104 A073303 A104211

Adjacent sequences: A116658 A116659 A116660 * A116662 A116663 A116664

Keyword

nonn

Author

Leroy Quet, Feb 21 2006

Extensions

More terms from Robert Gerbicz, Jun 09 2007

Status

approved