A109251 Number of numbers up to 10^n which are products of three primes.

0, 1, 22, 247, 2569, 25556, 250853, 2444359, 23727305, 229924367, 2227121996, 21578747909, 209214982913, 2030133769624, 19717814526785, 191693417109381, 1865380637252270, 18168907486812690, 177123437184971927, 1728190923820610000

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = A072114(10^n). - R. J. Mathar, May 25 2008

Example

There are 22 numbers with three prime factors up to 10^2: 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99.

Mathematica

ThreeAlmostPrimePi[n_] := Sum[ PrimePi[n/(Prime@i*Prime@j)] - j + 1, {i, PrimePi[n^(1/3)]}, {j, i, PrimePi@ Sqrt[n/Prime@i]}]; Table[ ThreeAlmostPrimePi[10^n], {n, 0, 14}] (* Robert G. Wilson v *)

Prog

(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot
def A109251(n):
    r = 10**n
    return int(sum(primepi(r//(k*m))-b for a, k in enumerate(primerange(integer_nthroot(r, 3)[0]+1)) for b, m in enumerate(primerange(k, isqrt(r//k)+1), a))) # Chai Wah Wu, Sep 18 2024

Crossrefs

Cf. A014612 = numbers with three prime factors, A036352 = number of numbers up to 10^n which are products of two primes, A072114.

Sequence in context: A125410 A200206 A252819 * A268791 A161521 A161900

Adjacent sequences: A109248 A109249 A109250 * A109252 A109253 A109254

Keyword

nonn

Author

Martin Raab, Aug 19 2005

Extensions

a(10)-a(14) from Robert G. Wilson v, Feb 06 2006

a(15)-a(17) from Hiroaki Yamanouchi, Aug 30 2014

a(18)-a(19) from Henri Lifchitz, Dec 01 2014

Status

approved