A205726 Number of semiprimes <= n^2.

0, 1, 3, 6, 9, 13, 17, 22, 26, 34, 40, 48, 56, 62, 75, 82, 90, 103, 114, 126, 135, 149, 164, 179, 190, 202, 220, 236, 253, 270, 289, 304, 320, 340, 360, 381, 404, 425, 443, 462, 484, 508, 533, 556, 581, 604, 634, 655, 678, 709, 738, 761, 783, 813, 846, 881

Offset: 1

Author

Keith Backman, Jan 30 2012

Keywords

• nonn

Comments

See A205727 and A205728 for related sequences and relationship to Goldbach conjecture.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358, A038108, A205727, A205728.

Programs

Mathematica

SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; nn = 100;  t = Select[Range[nn^2], SemiPrimeQ]; Table[Length[Select[t, # <= n^2 &]], {n, nn}] (* T. D. Noe, Jan 30 2012 *)
Module[{nn=60,sp},sp=Accumulate[Table[If[PrimeOmega[n]==2,1,0],{n,nn^2}]];Table[sp[[i^2]],{i,nn}]] (* Harvey P. Dale, May 29 2014 *)

Python

from sympy import prime, primepi
def A205726(n): return int(sum(primepi(n**2//prime(k))-k+1 for k in range(1,primepi(n)+1))) # Chai Wah Wu, Jul 23 2024

Formula

a(n) = A072000(A000290(n)). - Michel Marcus, Sep 02 2013