A205727 -id:A205727 - cp's OEIS frontend

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

Keith Backman, Jan 30 2012

nonn

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

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

Cf. A001358, A038108, A205727, A205728.

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 *)

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

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

A205728 Number of odd, nonsquare semiprimes <= n^2.

Original entry on oeis.org

0, 0, 0, 1, 2, 4, 5, 8, 11, 16, 19, 24, 28, 32, 41, 46, 50, 60, 66, 73, 81, 89, 100, 110, 118, 126, 140, 151, 163, 174, 187, 197, 210, 224, 239, 253, 269, 286, 298, 312, 326, 344, 363, 380, 399, 414, 435, 451, 468, 491, 513, 530, 546, 567, 591, 619, 643, 664

Offset: 1

Keith Backman, Jan 30 2012

nonn

Like A205727 (see comments thereto), this looks at odd semiprimes, but excludes squares. This then relates to the Goldbach conjecture 2j=p+q with the additional restriction that j, p, and q are not equal.

N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Cf. A205726, A205727.

SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; nn = 100;  t = Select[Range[1, nn^2, 2], SemiPrimeQ[#] && ! IntegerQ[Sqrt[#]] &]; Table[Length[Select[t, # <= n^2 &]], {n, nn}] (* T. D. Noe, Jan 30 2012 *)

cp's OEIS Frontend

A205726 Number of semiprimes <= n^2.

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