A036351 - OEIS

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, 833671466547121873095, 8056846659972421004731

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..23.

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

(Python)

from math import isqrt

from sympy import primepi, primerange

def A036351(n): return -(t:=primepi(s:=isqrt(m:=10**n)))-(t*(t-1)>>1)+sum(primepi(m//k) for k in primerange(1, s+1)) # Chai Wah Wu, Aug 15 2024

CROSSREFS

Cf. A066265.

Cf. A036352, A122121.

Sequence in context: A300685 A300608 A301350 * A189770 A245020 A277660

Adjacent sequences: A036348 A036349 A036350 * A036352 A036353 A036354

KEYWORD