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%I #18 Sep 08 2022 08:45:24
%S 4,6,8,9,10,12,18,20,22,25,27,32,34,44,48,49,50,58,68,72,80,82,108,
%T 116,118,121,125,128,142,162,164,165,169,176,192,200,202,214,236,242,
%U 243,272,273,274,284,288,289,298,320,343,345,358,361,382,385,394,399,404
%N Integers in both sequences A114522 and A063989.
%H Amiram Eldar, <a href="/A116661/b116661.txt">Table of n, a(n) for n = 1..10000</a>
%e 20 = 2^2 *5^1. Both the number of prime divisors (counted with multiplicity), 2+1 = 3 and the sum of the distinct prime divisors, 2+5 = 7, are primes. So 20 is in the sequence.
%t Select[Range[500],AllTrue[{PrimeOmega[#],Total[FactorInteger[#][[All, 1]]]}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 03 2019 *)
%o (Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; [k:k in [2..450]| IsPrime(f(k)) and IsPrime(&+PrimeDivisors(k))]; // _Marius A. Burtea_, Nov 14 2019
%Y Cf. A114522, A063989, A116660.
%K nonn
%O 1,1
%A _Leroy Quet_, Feb 21 2006
%E More terms from _Robert Gerbicz_, Jun 09 2007
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