A146168 Number of odd squarefree semiprimes (A036388) < 2^n.

0, 0, 0, 1, 2, 8, 20, 46, 96, 197, 404, 798, 1599, 3134, 6169, 12093, 23640, 46199, 90180, 176198, 343927, 671783, 1312304, 2564485, 5012807, 9803883, 19181677, 37545265, 73524262, 144038812, 282313035, 553557959, 1085860455

Offset

1,5

Links

Table of n, a(n) for n=1..33.

Formula

a(n) = A125527(n) - A000720(floor(sqrt(2^n))) - A007053(n-1) + 1.

Example

a(5)= 2. The semiprimes less than 2^5 are 15 and 21. Formula gives 10-pi(5)-pi(2^4)+1 = 2.

Mathematica

Table[lim=2^n; Sum[PrimePi[lim/p]-PrimePi[p], {p, Prime[Range[2, PrimePi[Sqrt[lim]]]]}], {n, 20}]

Crossrefs

Cf. A046388, A001358 (semiprimes), A000720 (pi(n), the number of primes <= n), A007053 (Number of primes <= 2^n), A125527 (Number of semiprimes <= 2^n).

Sequence in context: A203604 A240940 A066857 * A058405 A133326 A285185

Adjacent sequences: A146165 A146166 A146167 * A146169 A146170 A146171

Keyword

nonn

Author

Washington Bomfim, Oct 27 2008

Status

approved