A216593 Number of semiprimes among n-th million natural numbers.

210035, 197249, 193162, 190540, 188288, 187308, 185657, 184788, 183856, 183441, 182123, 181556, 181125, 180878, 180234, 179649, 179055, 178710, 178652, 178034, 178015, 177307, 177391, 177003, 176568, 176419, 176021, 175788, 175655, 175189, 174915, 175357

Offset

1,1

Comments

Let f(m) = number of semiprimes <m then a(n) is the number of semiprimes between 1+(n-1)*10^6 and n*10^6.

a(n) = 0 for almost all n. It seems infeasible to find the first such n. - Charles R Greathouse IV, Sep 09 2012

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Formula

a(n) ~ 1000000 n log log n / log n. - Charles R Greathouse IV, Sep 23 2012

Mathematica

f[m_] := Sum[ PrimePi[(m - 1)/Prime[i]], {i, PrimePi[ Sqrt[m]]}] - Binomial[ PrimePi[ Sqrt[m]], 2]; ta=Table[f[n*10^6], {n, 0, 1000}]; s=Rest[ta]-Most[ta] (* for first 1000 terms *)
(* using Mmca code by Robert G. Wilson v in A066265 - Zak Seidov, Sep 09 2012 *)

Prog

(PARI) a(n)=sum(k=10^6*(n-1), 10^6*n, bigomega(k)==2) \\ Charles R Greathouse IV, Sep 09 2012

Crossrefs

Cf. A001358, A036352, A064911, A066265, A072000.

Sequence in context: A232136 A183602 A015376 * A172825 A072760 A178421

Adjacent sequences: A216590 A216591 A216592 * A216594 A216595 A216596

Keyword

nonn

Author

Zak Seidov, Sep 09 2012

Status

approved