

A126589


Numbers n>1 such that prime of the form (n^k1)/(n1) does not exist for k>2; or A128164(n) = 0.


2



4, 9, 16, 25, 32, 36, 49, 64, 81, 100, 121, 125, 144, 169, 196, 216, 225, 243, 256, 289, 324, 343, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1000, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1728, 1764, 1849, 1936, 2025
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OFFSET

1,1


COMMENTS

Appears to be the union of the perfect squares k^2 (for k>1) and the prime powers p^k (for k>1) with some exceptions, such as 2^3, 3^3, 2^7, etc.
The perfect powers except those of the form n^(p^m) where p and (n^(p^(m+1))1)/(n^(p^m)1) are primes, p>2 and m>=1.  Max Alekseyev, Mar 09 2009


LINKS

Table of n, a(n) for n=1..51.
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927930.
Eric Weisstein's World of Mathematics, Repunit.


EXAMPLE

A128164 begins with offset 2: {3, 3, 0, 3, 3, 5, 3, 0, 19, 17, 3, 5, 3, 3, 0, 3, ...}. Thus a(1) = 4, a(2) = 9, a(3) = 16.


CROSSREFS

Cf. A128164, A084738, A065854, A084740, A084741, A065507, A084742.
Sequence in context: A010433 A175592 A331219 * A010409 A010457 A244833
Adjacent sequences: A126586 A126587 A126588 * A126590 A126591 A126592


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Mar 13 2007


EXTENSIONS

Extended by Max Alekseyev, Mar 09 2009


STATUS

approved



