OFFSET
1,1
COMMENTS
Computed up to 10^19 by program. The program was written in C, and is rather long. It starts by finding all prime numbers up to 4*10^9, then uses that to count all powers of these primes up to 10^19.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..48
Daniel Mondot, Math puzzle about Least Common Multiple (french:PPCM)
EXAMPLE
For n=1, there are 3 powers of prime numbers less than 10^1: 2^2, 2^3 and 3^2. i.e. 4, 8, 9.
For n=2, there are 10 powers of prime numbers less than 10^2: 4, 8, 9, 16, 25, 27, 32, 49, 64, 81.
MATHEMATICA
a[n_] := Sum[PrimePi [10^(n/k)], {k, 2, n * Log2[10]}]; Array[a, 20] (* Giovanni Resta, Apr 09 2016 *)
PROG
(SageMath)
def A267574(n):
gen = (p for p in srange(2, 10^n) if p.is_prime_power() and not p.is_prime())
return sum(1 for _ in gen)
print([A267574(n) for n in range(1, 7)]) # Peter Luschny, Sep 16 2023
(Python)
from sympy import primepi, integer_nthroot
def A267574(n): return int(sum(primepi(integer_nthroot(10**n, k)[0]) for k in range(2, (10**n).bit_length()))) # Chai Wah Wu, Aug 14 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Daniel Mondot, Jan 17 2016
EXTENSIONS
a(20)-a(26) from Chai Wah Wu, Jan 25 2016
a(27)-a(34) from Giovanni Resta, Apr 09 2016
STATUS
approved