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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A046363, A000961, A008472.

Sequence in context: A262481 A119689 A351614 * A242100 A125592 A292431

Adjacent sequences: A066035 A066036 A066037 * A066039 A066040 A066041

Keyword

nonn

Author

Joseph L. Pe, Dec 12 2001

Extensions

More terms from Vladeta Jovovic, Dec 13 2001

Status

approved