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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
OFFSET
1,1
COMMENTS
No multiples of 4 because subsequence of A048103.
LINKS
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
Subsequence of A048103 and of A099308.
Sequence in context: A212047 A244034 A154864 * A186120 A065343 A222576
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 10 2019
STATUS
approved