A107352 Number of positive integers <= 10^n that are divisible by no prime exceeding 11.

1, 10, 55, 192, 522, 1197, 2432, 4520, 7838, 12867, 20193, 30524, 44696, 63694, 88658, 120895, 161885, 213294, 276997, 355082, 449849, 563834, 699826, 860861, 1050260, 1271598, 1528765, 1825937, 2167611, 2558606, 3004075, 3509523

Offset

0,2

Comments

Lehmer quotes A. E. Western as computing a(5) = 1197, a(8) = 7838 and a(10) = 20193.

Number of integers of the form 2^a*3^b*5^c*7^d*11^e <= 10^n.

Links

David A. Corneth, Table of n, a(n) for n = 0..119

D. H. Lehmer, The lattice points of an n-dimensional tetrahedron, Duke Math. J., 7 (1941), 341-353.

Formula

Does a(n)/(a(n-1) - a(n-2)) tend to c*n + d for large n where c ~= 0.20 and d ~= 1.37? - David A. Corneth, Nov 14 2019

Mathematica

fQ[n_] := FactorInteger[n][[ -1, 1]] < 13; c = 1; k = 1; Do[ While[k <= 10^n, If[ fQ[k], c++ ]; k++ ]; Print[c], {n, 0, 9}] (* Or *)
n = 32; t = Select[ Flatten[ Table[11^e*Select[ Flatten[ Table[7^d*Select[ Flatten[ Table[5^c*Select[ Flatten[ Table[2^a*3^b, {a, 0, Log[2, 10^n]}, {b, 0, Log[3, 10^n]}]], # <= 10^n &], {c, 0, Log[5, 10^n]}]], # <= 10^n &], {d, 0, Log[7, 10^n]}]], # <= 10^n &], {e, 0, Log[11, 10^n]}]], # <= 10^n &]; Table[ Length[ Select[t, # <= 10^n &]], {n, 0, 32}] (* Robert G. Wilson v, May 24 2005 *)

Prog

(Python)
from sympy import integer_log, prevprime
def A107352(n):
    def g(x, m): return sum((x//3**i).bit_length() for i in range(integer_log(x, 3)[0]+1)) if m==3 else sum(g(x//(m**i), prevprime(m))for i in range(integer_log(x, m)[0]+1))
    return g(10**n, 11) # Chai Wah Wu, Oct 22 2024

Crossrefs

Row 5 of A253635.

Cf. A011557, A051038.

Sequence in context: A321780 A074977 A069155 * A127761 A337898 A357730

Adjacent sequences: A107349 A107350 A107351 * A107353 A107354 A107355

Keyword

nonn

Author

N. J. A. Sloane, May 23 2005

Extensions

More terms from Robert G. Wilson v and Don Reble, May 26 2005

Status

approved