A106600 Number of positive integers <= 10^n that are divisible by no prime exceeding 7.

1, 10, 46, 141, 338, 694, 1273, 2155, 3427, 5194, 7575, 10688, 14672, 19674, 25861, 33406, 42487, 53302, 66061, 80988, 98311, 118271, 141124, 167139, 196597, 229785, 267007, 308575, 354820, 406074, 462692, 525030, 593467, 668384, 750177, 839260

Offset

0,2

Comments

Position of 10^n among the 7-smooth numbers (A002473). Note that all powers of 10 are in A002473. - Zak Seidov, Nov 18 2013

Links

Zak Seidov, Table of n, a(n) for n = 0..200

Example

A002473(a(2)) = A002473(46)=100.

Mathematica

n = 35; t = 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[5, 10]}]], # <= 10^n &]; Table[ Length[ Select[t, # <= 10^n &]], {n, 0, 35}]

Prog

(Python)
from sympy import integer_log
def A106600(n):
    ptuple = (2, 3, 5, 7)
    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, 3) # Chai Wah Wu, Mar 16 2026

Crossrefs

Row 4 of A253635.

Cf. A002473, A011557.

Sequence in context: A288117 A213834 A241084 * A085437 A024166 A103501

Adjacent sequences: A106597 A106598 A106599 * A106601 A106602 A106603

Keyword

nonn

Author

Robert G. Wilson v, May 27 2005

Status

approved