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%I #22 Sep 08 2022 08:45:23
%S 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,
%T 34,36,37,40,41,43,44,47,48,49,50,53,54,58,59,61,64,67,68,71,72,73,79,
%U 80,81,82,83,88,89,96,97,100,101,103,107,108,109,113,116,118,121,125,127
%N Numbers n such that sum of distinct prime divisors of n is prime.
%C Sequence is the union of the primes and sequence A047820.
%H Amiram Eldar, <a href="/A114522/b114522.txt">Table of n, a(n) for n = 1..10000</a>
%e 24 = 2^3 * 3 and 2 + 3 = 5, which is prime. So 24 is included.
%t f[n_] := Plus @@ First /@ FactorInteger[n]; Select[Range[130], PrimeQ[f[ # ]] &] (* _Ray Chandler_, Dec 07 2005 *)
%t Select[Range@127, PrimeQ[Plus @@ First /@ FactorInteger@# ] &] (* _Robert G. Wilson v_, Dec 07 2005 *)
%o (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
%o (Magma) [k:k in [2..150]| IsPrime(&+PrimeDivisors(k))]; // _Marius A. Burtea_, Oct 06 2019
%Y Cf. A000079, A003586, A003592.
%Y Cf. A008472, A047820, A108605, A114518.
%K nonn
%O 1,1
%A _Leroy Quet_, Dec 05 2005
%E Extended by _Robert G. Wilson v_, _Ray Chandler_ and Lambert Herrgesell (zero815(AT)googlemail.com), Dec 07 2005
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