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A128952 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 the prime 3 and is not divisible by at least one of the primes 2, 5 and 7.

%I A128952 #26 May 10 2025 03:08:24
%S A128952 66,657,6572,65715,657143,6571429,65714286,657142857,6571428572,
%T A128952 65714285715,657142857143,6571428571429,65714285714286,
%U A128952 657142857142857,6571428571428572,65714285714285715,657142857142857143,6571428571428571429,65714285714285714286,657142857142857142857
%N A128952 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 the prime 3 and is not divisible by at least one of the primes 2, 5 and 7.
%H A128952 Vincenzo Librandi, <a href="/A128952/b128952.txt">Table of n, a(n) for n = 2..1000</a>
%H A128952 Milan Janjic, <a href="https://old.pmf.unibl.org/wp-content/uploads/2017/10/enumfun.pdf">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A128952 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (11,-11,11,-11,11,-10).
%F A128952 a(n) = 10^n - floor(10^n/3) - floor(10^n/70) + floor(10^n/210).
%F A128952 From _Chai Wah Wu_, May 09 2025: (Start)
%F A128952 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 A128952 G.f.: x^2*(-70*x^5 + 69*x^4 - 76*x^3 + 71*x^2 - 69*x + 66)/((x - 1)*(10*x - 1)*(x^2 - x + 1)*(x^2 + x + 1)). (End)
%e A128952 a(6) = 10^6 - floor(10^6/3) - floor(10^6/70) + floor(10^6/210) = 1000000 - floor(333333.333...) - floor(14285.714...) + floor(4761.904...) = 1000000 - 333333 - 14285 + 4761 = 657143. - _Jon E. Schoenfield_, Nov 18 2018
%p A128952 a := n->10^n-floor(10^n/3)-floor(10^n/70)+floor(10^n/210);
%t A128952 Table[With[{c=10^n},c-Floor[c/3]-Floor[c/70]+Floor[c/210]],{n,2,20}] (* _Harvey P. Dale_, Jun 22 2022 *)
%o A128952 (Magma) [10^n-Floor(10^n/3)-Floor(10^n/70)+Floor(10^n/210): n in [2..20]]; // _Vincenzo Librandi_, Oct 02 2011
%Y A128952 Cf. A092695.
%K A128952 nonn
%O A128952 2,1
%A A128952 _Milan Janjic_, Apr 28 2007