A066265 - OEIS

(PARI) a(n)=my(s); forprime(p=2, sqrt(10^n), s+=primepi((10^n-1)\p)); s-binomial(primepi(sqrt(10^n)), 2) \\ Charles R Greathouse IV, Apr 23 2012

(Perl) use Math::Prime::Util qw/:all/; use integer; sub countsp { my($k, $sum, $pc)=($_[0]-1, 0, 1); prime_precalc(60_000_000); forprimes { $sum += prime_count($k/$_) + 1 - $pc++; } int(sqrt($k)); $sum; } foreach my $n (0..16) { say "$n: ", countsp(10**$n); } # Dana Jacobsen, May 11 2014

(Python)

from math import isqrt

from sympy import primepi, primerange

def A066265(n): return int((-(t:=primepi(s:=isqrt(m:=10**n)))*(t-1)>>1)+sum(primepi(m//k) for k in primerange(1, s+1))) if n>1 else 3*n # Chai Wah Wu, Aug 16 2024