A205726 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

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

FORMULA

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

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 *)

PROG

(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

CROSSREFS

Cf. A001358, A038108, A205727, A205728.

Sequence in context: A256966 A280944 A330321 * A002815 A342711 A109512

Adjacent sequences: A205723 A205724 A205725 * A205727 A205728 A205729

KEYWORD

nonn

AUTHOR

Keith Backman, Jan 30 2012

STATUS

approved