A128957 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 at least one of the primes 2,5 and is not divisible by at least one of the primes 3,7.

86, 857, 8571, 85715, 857142, 8571429, 85714286, 857142857, 8571428571, 85714285715, 857142857142, 8571428571429, 85714285714286, 857142857142857, 8571428571428571, 85714285714285715, 857142857142857142

Offset: 2

Author

Milan Janjic, Apr 28 2007

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..1000
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Crossrefs

Cf. A092695.

Programs

Magma

[10^n-Floor(10^n/10)-Floor(10^n/21)+Floor(10^n/210): n in [2..20]]; // Vincenzo Librandi, Oct 02 2011

Maple

f := n->10^n-floor(10^n/10)-floor(10^n/21)+floor(10^n/210);

Formula

a(n) = 10^n - floor(10^n/10) - floor(10^n/21) + floor(10^n/210).

Conjectures from Colin Barker, Nov 06 2017: (Start)

G.f.: x^2*(86 + 83*x + 84*x^2 + 89*x^3 + 81*x^4 + 90*x^5) / ((1 + x)*(1 - 10*x)*(1 - x + x^2)*(1 + x + x^2)).

a(n) = 9*a(n-1) + 9*a(n-2) + 9*a(n-3) + 9*a(n-4) + 9*a(n-5) + 10*a(n-6) for n>7.

(End)