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
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
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Magma
[10^n-Floor(10^n/6)-Floor(10^n/35)+Floor(10^n/210): n in [2..20]]; // Vincenzo Librandi, Oct 02 2011
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Maple
f := n->10^n-floor(10^n/2)-floor(10^n/35)+floor(10^n/210);
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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
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)