A114522 Numbers n such that sum of distinct prime divisors of n is prime.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 22, 23, 24, 25, 27, 29, 31, 32, 34, 36, 37, 40, 41, 43, 44, 47, 48, 49, 50, 53, 54, 58, 59, 61, 64, 67, 68, 71, 72, 73, 79, 80, 81, 82, 83, 88, 89, 96, 97, 100, 101, 103, 107, 108, 109, 113, 116, 118, 121, 125, 127

Offset

1,1

Comments

Sequence is the union of the primes and sequence A047820.

Links

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

Example

24 = 2^3 * 3 and 2 + 3 = 5, which is prime. So 24 is included.

Mathematica

f[n_] := Plus @@ First /@ FactorInteger[n]; Select[Range[130], PrimeQ[f[ # ]] &] (* Ray Chandler, Dec 07 2005 *)
Select[Range@127, PrimeQ[Plus @@ First /@ FactorInteger@# ] &] (* Robert G. Wilson v, Dec 07 2005 *)

Prog

(PARI) for(n=1, 200, v=factor(n); s=0; for(i=1, matsize(v)[1], s+=v[i, 1]); if(isprime(s), print1(n, ", "))) \\ Lambert Herrgesell (zero815(AT)googlemail.com), Dec 07 2005
(Magma) [k:k in [2..150]| IsPrime(&+PrimeDivisors(k))]; // Marius A. Burtea, Oct 06 2019

Crossrefs

Cf. A000079, A003586, A003592.

Cf. A008472, A047820, A108605, A114518.

Sequence in context: A262524 A102450 A023782 * A283657 A053432 A349999

Adjacent sequences: A114519 A114520 A114521 * A114523 A114524 A114525

Keyword

nonn

Author

Leroy Quet, Dec 05 2005

Extensions

Extended by Robert G. Wilson v, Ray Chandler and Lambert Herrgesell (zero815(AT)googlemail.com), Dec 07 2005

Status

approved