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A146167
Number of odd squarefree semiprimes (A046388) <= n.
2
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
1,21
COMMENTS
A346622 is a different although very similar sequence. - N. J. A. Sloane, Aug 23 2021
FORMULA
a(n) = A072000(n) - A000720(floor(sqrt(n))) - A000720(floor(n/2)) + 1.
EXAMPLE
a(33)= 3. The semiprimes <=33 are 15, 21 and 33. Formula gives 11-pi(5)-pi(16)+1 = 3.
MATHEMATICA
Accumulate[Table[If[OddQ[n]&&SquareFreeQ[n]&&PrimeOmega[n]==2, 1, 0], {n, 0, 100}]] (* Harvey P. Dale, Feb 08 2016 *)
PROG
(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
CROSSREFS
Cf. A046388, A001358 (semiprimes), A072000 (Number of semiprimes <= n), A000720 (pi(n), the number of primes <= n).
Cf. also A346622.
Sequence in context: A279758 A082996 A094382 * A346622 A103380 A309120
KEYWORD
nonn
AUTHOR
Washington Bomfim, Oct 27 2008
STATUS
approved