A244508 Number of odd prime powers (A246655) between 2^n and 2^(n+1).

0, 1, 2, 3, 7, 8, 16, 25, 46, 80, 141, 263, 473, 882, 1628, 3044, 5734, 10779, 20428, 38687, 73653, 140425, 268340, 513866, 986033, 1894409, 3646134, 7027825, 13562625, 26208248, 50698865, 98184467, 190338061, 369326690, 717271793, 1394198586, 2712112561

Offset: 0

Author

Michel Marcus, Nov 17 2014

Keywords

• nonn

Examples

			Between 2 and 4, there is just 1 prime power: 3, so a(1) = 1.
Between 4 and 8, there are 2 prime powers: 5 and 7, so a(2) = 2.
		

Links

• Ray Chandler, Table of n, a(n) for n = 0..91 (using b-file from A007053, corrected n = 45..52, n = 0..52 from Hiroaki Yamanouchi)

Crossrefs

Cf. A246655 (prime powers), A182908 (positions of 2^n among prime powers).

Programs

Mathematica

Table[Count[Range[2^n + 1, 2^(n + 1) - 1], ?PrimePowerQ], {n, 0, 27}] (* _Ivan N. Ianakiev, Nov 18 2014 *)

PARI

a(n) = sum(i=2^n+1, 2^(n+1)-1, isprimepower(i)>0);

Python

from sympy import primepi, integer_nthroot
def A244508(n):
    def f(x): return int(1+sum(primepi(integer_nthroot(x, k)[0]) for k in range(1, x.bit_length())))
    return f((1<Chai Wah Wu, Nov 05 2024

Formula

a(n) = A182908(n+1) - A182908(n). - Ray Chandler, Aug 20 2021

Extensions

a(28)-a(36) from Hiroaki Yamanouchi, Nov 20 2014

Minor edits by Ray Chandler, Aug 20 2021