A146167 Number of odd squarefree semiprimes (A046388) <= n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11

Offset: 1

Author

Washington Bomfim, Oct 27 2008

Keywords

• nonn

Comments

A346622 is a different although very similar sequence. - N. J. A. Sloane, Aug 23 2021

Examples

			a(33)= 3. The semiprimes <=33 are 15, 21 and 33. Formula gives 11-pi(5)-pi(16)+1 = 3.
		

Crossrefs

Cf. A046388, A001358 (semiprimes), A072000 (Number of semiprimes <= n), A000720 (pi(n), the number of primes <= n).

Cf. also A346622.

Programs

Mathematica

Accumulate[Table[If[OddQ[n]&&SquareFreeQ[n]&&PrimeOmega[n]==2,1,0],{n,0,100}]] (* Harvey P. Dale, Feb 08 2016 *)

Python

from math import isqrt
from sympy import prime, primepi
def A146167(n): return int(sum(primepi(n//prime(k))-k+1 for k in range(2,primepi(isqrt(n))+1)))-primepi(isqrt(n))+1 if n>3 else 0 # Chai Wah Wu, Jul 23 2024

Formula

a(n) = A072000(n) - A000720(floor(sqrt(n))) - A000720(floor(n/2)) + 1.