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Numbers with at least two prime factors such that the sum of the prime factors is prime.
3

%I #18 Dec 15 2018 09:46:39

%S 6,10,12,18,20,22,24,34,36,40,44,48,50,54,58,68,72,80,82,88,96,100,

%T 108,116,118,136,142,144,160,162,164,165,176,192,200,202,210,214,216,

%U 232,236,242,250,272,273,274,284,288,298,320,324,328,345,352,358,382,384

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

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

%H Harry J. Smith, <a href="/A066038/b066038.txt">Table of n, a(n) for n = 1..1000</a>

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

%t 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 *)

%o (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

%o (PARI) isok(n) = (omega(n) > 1) && isprime(vecsum(factor(n)[,1])); \\ _Michel Marcus_, Dec 15 2018

%Y Cf. A046363, A000961, A008472.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Dec 12 2001

%E More terms from _Vladeta Jovovic_, Dec 13 2001