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A328239 Numbers whose third arithmetic derivative (A099306) is prime. 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 26 13:59 EDT 2022. Contains 354092 sequences. (Running on oeis4.)