A100752 a(n) is the number of positive integers <= 10^n that are divisible by no prime exceeding 3.

1, 7, 20, 40, 67, 101, 142, 190, 244, 306, 376, 452, 534, 624, 720, 824, 935, 1052, 1178, 1309, 1447, 1593, 1745, 1905, 2071, 2244, 2424, 2611, 2806, 3006, 3214, 3429, 3652, 3881, 4117, 4360, 4610, 4866, 5131, 5401, 5679, 5964, 6255, 6553, 6859, 7172, 7491

Offset: 0

Author

Robert G. Wilson v, May 27 2005

Keywords

• nonn

Comments

A good approximation seems to be ceiling(log(10^n)*log(6*10^n)/(log(3)*log(4))). - Horst H. Manninger, Oct 29 2022

Examples

			a(1) = 7 as there are 7 3-smooth numbers less than 10^1 = 10; they are 1, 2, 3, 4, 6, 8, 9. - _David A. Corneth_, Nov 14 2019
		

Links

• David A. Corneth, Table of n, a(n) for n = 0..1999

Crossrefs

Cf. A003586, A011557, A071521.

Cf. A066343, A106598, A106600, A107352, A106629.

Row 2 of A253635.

Programs

Mathematica

f[n_] := Sum[ Floor@ Log[2, n/3^i] + 1, {i, 0, Log[3, n]}]; Table[ f[10^n], {n, 0, 46}] (* Robert G. Wilson v, Nov 07 2012 *)

Python

from sympy import integer_log
def A100752(n): return sum((10**n//3**i).bit_length() for i in range(integer_log(10**n,3)[0]+1)) # Chai Wah Wu, Oct 23 2024

Formula

a(n) = A071521(10^n). - Chai Wah Wu, Oct 23 2024