OFFSET
0,3
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)
FORMULA
EXAMPLE
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.
MATHEMATICA
Table[Count[Range[2^n + 1, 2^(n + 1) - 1], _?PrimePowerQ], {n, 0, 27}] (* Ivan N. Ianakiev, Nov 18 2014 *)
PROG
(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<<n+1)-1)-f((1<<n)) # Chai Wah Wu, Nov 05 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Nov 17 2014
EXTENSIONS
a(28)-a(36) from Hiroaki Yamanouchi, Nov 20 2014
Minor edits by Ray Chandler, Aug 20 2021
STATUS
approved