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A164345
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Powers of primes where the exponents are not powers of primes.
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2
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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
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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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
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EXAMPLE
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2^12 = 4096. Since 2 is prime, and since 12 is not a power of a prime, then 4096 is in this sequence.
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PROG
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(PARI) isok(k) = if(k==1, return(1)); my(q=isprimepower(k)); (q>1) && !isprimepower(q); \\ Michel Marcus, Nov 26 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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