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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
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
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
KEYWORD
nonn
AUTHOR
Leroy Quet, Aug 13 2009
EXTENSIONS
Extended beyond 16384 by R. J. Mathar, Sep 27 2009
STATUS
approved