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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.

%I A128959 #18 Sep 08 2022 08:45:30
%S A128959 82,810,8096,80953,809524,8095239,80952382,809523810,8095238096,
%T A128959 80952380953,809523809524,8095238095239,80952380952382,
%U A128959 809523809523810,8095238095238096,80952380952380953,809523809523809524,8095238095238095239,80952380952380952382
%N 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.
%H A128959 Vincenzo Librandi, <a href="/A128959/b128959.txt">Table of n, a(n) for n = 2..1000</a>
%H A128959 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A128959 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (11,-11,11,-11,11,-10).
%F A128959 a(n) = 10^n-floor(10^n/6)-floor(10^n/35)+floor(10^n/210).
%F A128959 From _Colin Barker_, Nov 17 2015: (Start)
%F A128959 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.
%F A128959 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)).
%F A128959 (End)
%p A128959 f := n->10^n-floor(10^n/2)-floor(10^n/35)+floor(10^n/210);
%o A128959 (Magma) [10^n-Floor(10^n/6)-Floor(10^n/35)+Floor(10^n/210): n in [2..20]]; // _Vincenzo Librandi_, Oct 02 2011
%o A128959 (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
%Y A128959 Cf. A092695.
%K A128959 nonn,easy
%O A128959 2,1
%A A128959 _Milan Janjic_, Apr 28 2007