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

Author

Leroy Quet, Aug 13 2009

Keywords

• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A024619, A096165 (complement with respect to A000961), A164337.

Programs

PARI

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

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

Extensions

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