A146168 Number of odd squarefree semiprimes (A046388) < 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, 2130904274, 4183364732, 8215861037

Offset: 1

Author

Washington Bomfim, Oct 27 2008

Keywords

• nonn

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..57 (calculated using the b-files at A060967, A007053 and A125527)

Crossrefs

Cf. A046388, A001358 (semiprimes), A000720 (pi(n), the number of primes <= n), A007053 (number of primes <= 2^n), A060967, A125527 (number of semiprimes <= 2^n).

Programs

Mathematica

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

Formula

a(n) = A125527(n) - A060967(n) - A007053(n-1) + 1, for n > 1.

Extensions

a(34) onwards from Amiram Eldar, Sep 05 2024