A146167 - OEIS

%I #13 Jul 23 2024 15:46:03

%S 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,

%T 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,

%U 10,10,10,10,10,10,10,10,11

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

%C A346622 is a different although very similar sequence. - _N. J. A. Sloane_, Aug 23 2021

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

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

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

%o (Python)

%o from math import isqrt

%o from sympy import prime, primepi

%o 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

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

%Y Cf. also A346622.

%K nonn

%O 1,21

%A _Washington Bomfim_, Oct 27 2008