A304521 a(n) is the number of prime powers k such that ceiling(log_2(k)) = n.

1, 2, 3, 4, 8, 9, 17, 26, 47, 81, 142, 264, 474, 883, 1629, 3045, 5735, 10780, 20429, 38688, 73654, 140426, 268341, 513867, 986034, 1894410, 3646135, 7027826, 13562626, 26208249, 50698866, 98184468, 190338062, 369326691, 717271794, 1394198587, 2712112562

Offset: 1

Author

Jon E. Schoenfield, May 13 2018

Keywords

• nonn

Comments

Prime powers are defined as numbers of the form p^k with p prime and k >= 1 (A246655).

Examples

			a(1)=1 because the interval [2,2] contains 1 prime power: 2.
a(2)=2 because the interval [3,4] contains 2 prime powers: 3 and 4=2^2.
a(3)=3 because the prime powers in [5,8] are 5, 7, and 8=2^3.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..92

Crossrefs

Cf. A029837, A036378, A246655.

Programs

PARI

a(n) = sum(k=2^(n-1)+1, 2^n, isprimepower(k) != 0); \\ Michel Marcus, May 17 2018

Python

from sympy import primepi, integer_nthroot
def A304521(n):
    def f(x):
        m = 1<Chai Wah Wu, Jan 19 2025