A106629 Number of positive integers <= 10^n that are divisible by no prime exceeding 13.

1, 10, 62, 242, 733, 1848, 4106, 8289, 15519, 27365, 45914, 73908, 114831, 173077, 254065, 364385, 511985, 706293, 958460, 1281500, 1690506, 2202871, 2838489, 3620013, 4573071, 5726533, 7112760, 8767880, 10732089, 13049906, 15770500, 18948010, 22641849, 26917042, 31844560

Offset

0,2

Links

Chai Wah Wu, Table of n, a(n) for n = 0..372

Mathematica

n = 10; t = Select[ Flatten[ Table[13^f*Select[ Flatten[ Table[11^e*Select[ Flatten[ Table[7^d*Select[ Flatten[ Table[5^c*Select[ Flatten[ Table[2^a*3^b, {a, 0, n*Log[2, 10]}, {b, 0, n*Log[3, 10]}]], # <= 10^n &], {c, 0, n*Log[5, 10]}]], # <= 10^n &], {d, 0, n*Log[7, 10]}]], # <= 10^n &], {e, 0, n*Log[11, 10]}]], # <= 10^n &], {f, 0, n*Log[13, 10]}]], # <= 10^n &]; Table[ Length[ Select[t, # <= 10^n &]], {n, 0, 10}];

Prog

(Python)
from sympy import integer_log
def A106629(n):
    ptuple = (2, 3, 5, 7, 11, 13)
    def g(x, m): return sum(g(x//(ptuple[m]**i), m-1)for i in range(integer_log(x, ptuple[m])[0]+1)) if m else x.bit_length()
    return g(10**n, 5) # Chai Wah Wu, Mar 16 2026

Crossrefs

Row 6 of A253635.

Cf. A011557, A080197.

Sequence in context: A015867 A297863 A298130 * A240157 A350644 A196632

Adjacent sequences: A106626 A106627 A106628 * A106630 A106631 A106632

Keyword

nonn

Author

Robert G. Wilson v, May 27 2005

Extensions

a(21)-a(34) from Daniel Suteu, Nov 14 2019

Status

approved