A036351 Number of numbers <= 10^n that are products of two distinct primes.

2, 30, 288, 2600, 23313, 209867, 1903878, 17426029, 160785135, 1493766851, 13959963049, 131125938680, 1237087821006, 11715901643501, 111329815346924, 1061057287065814, 10139482896634686, 97123037634329553, 932300026078297246, 8966605849186166511, 86389956292394285653

Offset

1,1

Links

Table of n, a(n) for n=1..21.

Index entries for sequences related to numbers of primes in various ranges

Formula

a(n) = (1/2)*(pi(10^(n/2)) + Sum_{i=1..pi(10^n)} pi((10^n-1)/P_i)) -1 = Sum_{i=1..pi(sqrt(10^n))} (pi((10^n-1)/P_i) -1) - binomial(pi(sqrt(10^n)), 2). - Robert G. Wilson v, May 19 2005

a(n) = A036352(n) - A122121(n). - Robert G. Wilson v, Feb 07 2012

Mathematica

f[n_] := Sum[ PrimePi[n/Prime[i]] - i, {i, PrimePi[ Sqrt[ n]] }]; Table[ f[10^n], {n, 14}] (* Robert G. Wilson v, Feb 07 2012 and modified Dec 28 2016 *)

Prog

(PARI) a(n)=my(s); forprime(p=2, sqrt(10^n), s+=primepi(10^n\p)); s-binomial(primepi(sqrt(10^n))+1, 2) \\ Charles R Greathouse IV, Apr 23 2012

Crossrefs

Cf. A066265.

Cf. A036352, A122121.

Sequence in context: A300685 A300608 A301350 * A189770 A245020 A277660

Adjacent sequences: A036348 A036349 A036350 * A036352 A036353 A036354

Keyword

nonn

Author

Shyam Sunder Gupta

Extensions

a(14) from Robert G. Wilson v, May 19 2005

a(15)-a(16) from Donovan Johnson, Oct 16 2010

Corrected a(15) and a(16) by Henri Lifchitz, Nov 11 2012

a(17)-a(19) from Henri Lifchitz, Nov 11 2012

a(20)-a(21) from Henri Lifchitz, Jul 03 2015

Status

approved