A128952 a(n) is equal to the number of positive integers m less than or equal to 10^n such that m is not divisible by the prime 3 and is not divisible by at least one of the primes 2, 5 and 7.

66, 657, 6572, 65715, 657143, 6571429, 65714286, 657142857, 6571428572, 65714285715, 657142857143, 6571428571429, 65714285714286, 657142857142857, 6571428571428572, 65714285714285715, 657142857142857143, 6571428571428571429, 65714285714285714286, 657142857142857142857

Offset: 2

Author

Milan Janjic, Apr 28 2007

Keywords

• nonn

Examples

			a(6) = 10^6 - floor(10^6/3) - floor(10^6/70) + floor(10^6/210) = 1000000 - floor(333333.333...) - floor(14285.714...) + floor(4761.904...) = 1000000 - 333333 - 14285 + 4761 = 657143. - _Jon E. Schoenfield_, Nov 18 2018
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..1000
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
• Index entries for linear recurrences with constant coefficients, signature (11,-11,11,-11,11,-10).

Crossrefs

Cf. A092695.

Programs

Magma

[10^n-Floor(10^n/3)-Floor(10^n/70)+Floor(10^n/210): n in [2..20]]; // Vincenzo Librandi, Oct 02 2011

Maple

a := n->10^n-floor(10^n/3)-floor(10^n/70)+floor(10^n/210);

Mathematica

Table[With[{c=10^n},c-Floor[c/3]-Floor[c/70]+Floor[c/210]],{n,2,20}] (* Harvey P. Dale, Jun 22 2022 *)

Formula

a(n) = 10^n - floor(10^n/3) - floor(10^n/70) + floor(10^n/210).

From Chai Wah Wu, May 09 2025: (Start)

a(n) = 11*a(n-1) - 11*a(n-2) + 11*a(n-3) - 11*a(n-4) + 11*a(n-5) - 10*a(n-6) for n > 7.

G.f.: x^2*(-70*x^5 + 69*x^4 - 76*x^3 + 71*x^2 - 69*x + 66)/((x - 1)*(10*x - 1)*(x^2 - x + 1)*(x^2 + x + 1)). (End)