A085501 - OEIS

A085501

Number of prime powers p^k <= n that are not prime (k = 0 or k > 1).

1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

a(n) = Max{k: A025475(k)<=n};

a(n)=A065515(n)-A000720(n)=A069637(n)+1;

for n<36=(2*3)^2: a(n) = A069623(n).

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Prime Power.

Eric Weisstein's World of Mathematics, Perfect Powers.

PROG

(PARI) a(n)=sum(k=2, logint(n, 2), primepi(sqrtnint(n, k)))+1 \\ Charles R Greathouse IV, Jul 21 2017

(PARI) first(n)=my(v=vector(n), s=1); for(e=2, logint(n, 2), forprime(p=2, sqrtnint(n, e), v[p^e]=1)); for(i=1, n, s+=v[i]; v[i]=s); v \\ Charles R Greathouse IV, Jul 21 2017

(Python)

from sympy import primepi, integer_nthroot

def A085501(n): return 1+sum(primepi(integer_nthroot(n, k)[0]) for k in range(2, n.bit_length())) # Chai Wah Wu, Aug 15 2024

CROSSREFS

Sequence in context: A071136 A025425 A234451 * A069623 A076411 A217038

Adjacent sequences: A085498 A085499 A085500 * A085502 A085503 A085504

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Jul 03 2003

STATUS

approved