A328239 Numbers whose third arithmetic derivative (A099306) is prime.

14, 18, 38, 46, 138, 150, 166, 186, 258, 266, 322, 338, 342, 350, 398, 402, 502, 526, 530, 546, 550, 610, 626, 658, 662, 686, 717, 722, 725, 726, 734, 750, 758, 774, 826, 890, 931, 966, 970, 1002, 1034, 1074, 1110, 1126, 1166, 1175, 1178, 1190, 1258, 1262, 1294, 1302, 1338, 1366

Offset: 1

Author

Antti Karttunen, Oct 10 2019

Keywords

• nonn

Comments

No multiples of 4 because subsequence of A048103.

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A003415, A099306, A157037, A192192.

Subsequence of A048103 and of A099308.

Programs

Mathematica

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 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA328239(n) = isprime(A003415(A003415(A003415(n))));