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

1,1

Comments

No multiples of 4 because subsequence of A048103.

Links

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

Example

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

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 *)

Prog

(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))));

Crossrefs

Cf. A003415, A099306, A157037, A192192.

Subsequence of A048103 and of A099308.

Sequence in context: A212047 A244034 A154864 * A186120 A065343 A222576

Adjacent sequences: A328236 A328237 A328238 * A328240 A328241 A328242

Keyword

nonn

Author

Antti Karttunen, Oct 10 2019

Status

approved