%I #10 Oct 25 2019 16:57:49

%S 14,18,38,46,138,150,166,186,258,266,322,338,342,350,398,402,502,526,

%T 530,546,550,610,626,658,662,686,717,722,725,726,734,750,758,774,826,

%U 890,931,966,970,1002,1034,1074,1110,1126,1166,1175,1178,1190,1258,1262,1294,1302,1338,1366

%N Numbers whose third arithmetic derivative (A099306) is prime.

%C No multiples of 4 because subsequence of A048103.

%H Antti Karttunen, <a href="/A328239/b328239.txt">Table of n, a(n) for n = 1..10001</a>

%e A003415(A003415(A003415(14))) = 5, which is a prime, thus 14 is included in this sequence.

%t dn[0] = 0; dn[1] = 0; dn[n_?Negative] := -dn[-n]; dn[n_] := dn[n] = Module[{f = Transpose[ FactorInteger@n]}, If[ PrimeQ@n, 1, Total[n*f[[2]]/f[[1]]]]]; Select[Range@1390, PrimeQ@ dn@ dn@ dn@# &] (* _Robert G. Wilson v_, Oct 22 2019 *)

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o isA328239(n) = isprime(A003415(A003415(A003415(n))));

%Y Cf. A003415, A099306, A157037, A192192.

%Y Subsequence of A048103 and of A099308.

%K nonn

%O 1,1

%A _Antti Karttunen_, Oct 10 2019