A164345 Powers of primes where the exponents are not powers of primes.

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

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 A354178 A367803

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