

A164345


Powers of primes where the exponents are not powers of primes.


2



1, 64, 729, 1024, 4096, 15625, 16384, 32768, 59049, 117649, 262144, 531441, 1048576, 1771561, 2097152, 4194304, 4782969, 4826809, 9765625, 14348907, 16777216, 24137569, 47045881, 67108864, 148035889, 244140625, 268435456
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OFFSET

1,2


COMMENTS

First differs from A164337, after the initial 1 in this sequence: 2^64 = 18446744073709551616 is in sequence A164337, but is not in this sequence.
This sequence contains those powers of primes that are not in sequence A096165.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000


FORMULA

Sum_{n>=1} 1/a(n) = 1 + Sum_{k in A024619} P(k) = 1.018407114609068368636..., where P is the prime zeta function.  Amiram Eldar, Nov 26 2020


EXAMPLE

2^12 = 4096. Since 2 is prime, and since 12 is not a power of a prime, then 4096 is in this sequence.


PROG

(PARI) isok(k) = if(k==1, return(1)); my(q=isprimepower(k)); (q>1) && !isprimepower(q); \\ Michel Marcus, Nov 26 2020


CROSSREFS

Cf. A024619, A096165 (complement with respect to A000961), A164337.
Sequence in context: A161861 A179149 A074471 * A164337 A161860 A195249
Adjacent sequences: A164342 A164343 A164344 * A164346 A164347 A164348


KEYWORD

nonn


AUTHOR

Leroy Quet, Aug 13 2009


EXTENSIONS

Extended beyond 16384 by R. J. Mathar, Sep 27 2009


STATUS

approved



