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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.

%I A128957 #17 Sep 08 2022 08:45:30
%S A128957 86,857,8571,85715,857142,8571429,85714286,857142857,8571428571,
%T A128957 85714285715,857142857142,8571428571429,85714285714286,
%U A128957 857142857142857,8571428571428571,85714285714285715,857142857142857142
%N 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.
%H A128957 Vincenzo Librandi, <a href="/A128957/b128957.txt">Table of n, a(n) for n = 2..1000</a>
%H A128957 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%F A128957 a(n) = 10^n - floor(10^n/10) - floor(10^n/21) + floor(10^n/210).
%F A128957 Conjectures from _Colin Barker_, Nov 06 2017: (Start)
%F A128957 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)).
%F A128957 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.
%F A128957 (End)
%p A128957 f := n->10^n-floor(10^n/10)-floor(10^n/21)+floor(10^n/210);
%o A128957 (Magma) [10^n-Floor(10^n/10)-Floor(10^n/21)+Floor(10^n/210): n in [2..20]]; // _Vincenzo Librandi_, Oct 02 2011
%Y A128957 Cf. A092695.
%K A128957 nonn
%O A128957 2,1
%A A128957 _Milan Janjic_, Apr 28 2007