

A084746


Smallest k such that n^k  k is a prime, or 0 if no such number exists.


3



2, 1, 1, 2, 1, 2, 1, 2, 3, 18, 1, 2, 1, 2, 3, 6, 1, 2, 1, 2, 41, 110, 1, 18, 3, 2, 11, 2, 1, 24, 1, 2, 3, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


COMMENTS

Conjecture: no entry is zero.
If n is odd and greater than 3, k=a(n) is even. If n is an even composite number, k=a(n) is odd. For n>2, n and k=a(n) are coprime.  R. J. Mathar, Apr 02 2006, corrected by Farideh Firoozbakht, Aug 09 2014
a(36)>30000 or 0. a(37)..a(46) = 2, 1, 8, 3, 24, 1, 2, 1, 514, 6737.
If n1 is prime then a(n)=1.  Farideh Firoozbakht, Aug 09 2014


LINKS

Table of n, a(n) for n=2..35.


MAPLE

a := proc(n) local k; k := 1; while not isprime(n^kk) do k := k+1 od; k end: seq(a(n), n=2..35);


MATHEMATICA

f[n_] := Block[{k = 1}, If[OddQ[n], k++ ]; While[ ! PrimeQ[n^k  k], k += 2]; k]; Table[ f[n], {n, 3, 35}]


CROSSREFS

Cf. A084745.
Sequence in context: A230798 A266224 A029396 * A128259 A051194 A134838
Adjacent sequences: A084743 A084744 A084745 * A084747 A084748 A084749


KEYWORD

more,nonn


AUTHOR

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 15 2003


EXTENSIONS

Edited and extended by Robert G. Wilson v, Alec Mihailovs (Alec(AT)Mihailovs.com) and T. D. Noe, Jun 16 2003
Update on a(36) and a(46) from Max Alekseyev, Apr 24 2009


STATUS

approved



