A128959 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 2,3 and is not divisible by at least one of the primes 5,7.

82, 810, 8096, 80953, 809524, 8095239, 80952382, 809523810, 8095238096, 80952380953, 809523809524, 8095238095239, 80952380952382, 809523809523810, 8095238095238096, 80952380952380953, 809523809523809524, 8095238095238095239, 80952380952380952382

Offset

2,1

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).

Formula

a(n) = 10^n-floor(10^n/6)-floor(10^n/35)+floor(10^n/210).

From Colin Barker, Nov 17 2015: (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*(90*x^5-89*x^4+95*x^3-88*x^2+92*x-82) / ((x-1)*(10*x-1)*(x^2-x+1)*(x^2+x+1)).

(End)

Maple

f := n->10^n-floor(10^n/2)-floor(10^n/35)+floor(10^n/210);

Prog

(Magma) [10^n-Floor(10^n/6)-Floor(10^n/35)+Floor(10^n/210): n in [2..20]]; // Vincenzo Librandi, Oct 02 2011
(PARI) Vec(-x^2*(90*x^5-89*x^4+95*x^3-88*x^2+92*x-82)/((x-1)*(10*x-1)*(x^2-x+1)*(x^2+x+1)) + O(x^30)) \\ Colin Barker, Nov 17 2015

Crossrefs

Cf. A092695.

Sequence in context: A342832 A186688 A002309 * A305682 A317062 A230394

Adjacent sequences: A128956 A128957 A128958 * A128960 A128961 A128962

Keyword

nonn,easy

Author

Milan Janjic, Apr 28 2007

Status

approved