OFFSET
1,1
LINKS
FORMULA
a(n) = (1/2)*(pi(10^(n/2)) + Sum_{i=1..pi(10^n)} pi((10^n-1)/P_i)) -1 = Sum_{i=1..pi(sqrt(10^n))} (pi((10^n-1)/P_i) -1) - binomial(pi(sqrt(10^n)), 2). - Robert G. Wilson v, May 19 2005
MATHEMATICA
f[n_] := Sum[ PrimePi[n/Prime[i]] - i, {i, PrimePi[ Sqrt[ n]] }]; Table[ f[10^n], {n, 14}] (* Robert G. Wilson v, Feb 07 2012 and modified Dec 28 2016 *)
PROG
(PARI) a(n)=my(s); forprime(p=2, sqrt(10^n), s+=primepi(10^n\p)); s-binomial(primepi(sqrt(10^n))+1, 2) \\ Charles R Greathouse IV, Apr 23 2012
(Python)
from math import isqrt
from sympy import primepi, primerange
def A036351(n): return -(t:=primepi(s:=isqrt(m:=10**n)))-(t*(t-1)>>1)+sum(primepi(m//k) for k in primerange(1, s+1)) # Chai Wah Wu, Aug 15 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(14) from Robert G. Wilson v, May 19 2005
a(15)-a(16) from Donovan Johnson, Oct 16 2010
Corrected a(15) and a(16) by Henri Lifchitz, Nov 11 2012
a(17)-a(19) from Henri Lifchitz, Nov 11 2012
a(20)-a(21) from Henri Lifchitz, Jul 03 2015
STATUS
approved