A066038 Numbers with at least two prime factors such that the sum of the prime factors is prime.

6, 10, 12, 18, 20, 22, 24, 34, 36, 40, 44, 48, 50, 54, 58, 68, 72, 80, 82, 88, 96, 100, 108, 116, 118, 136, 142, 144, 160, 162, 164, 165, 176, 192, 200, 202, 210, 214, 216, 232, 236, 242, 250, 272, 273, 274, 284, 288, 298, 320, 324, 328, 345, 352, 358, 382, 384

Offset: 1

Author

Joseph L. Pe, Dec 12 2001

Keywords

• nonn

Comments

Numbers with just one prime factor (prime powers) trivially satisfy the defining condition and are not included.

Examples

			The prime factors of 12 are 2 and 3, which add up to 5, a prime.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A046363, A000961, A008472.

Programs

Mathematica

Reap[For[n = 6, n <= 1000, n++, pp = FactorInteger[n][[All, 1]]; If[Length[pp] >= 2 && PrimeQ[Total[pp]], Sow[n]]]][[2, 1]] (* Jean-François Alcover, Oct 16 2016 *)

PARI

sopf(n)= { local(f,s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); return(s) }
{ n=0; for (m=1, 10^9, if (omega(m) > 1 && isprime(sopf(m)), write("b066038.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Nov 07 2009

PARI

isok(n) = (omega(n) > 1) && isprime(vecsum(factor(n)[,1])); \\ Michel Marcus, Dec 15 2018

Extensions

More terms from Vladeta Jovovic, Dec 13 2001