A128950 - OEIS

%I #12 Sep 08 2022 08:45:30

%S 83,829,8286,82858,828571,8285715,82857143,828571429,8285714286,

%T 82857142858,828571428571,8285714285715,82857142857143,

%U 828571428571429,8285714285714286,82857142857142858,828571428571428571

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

%H Vincenzo Librandi, <a href="/A128950/b128950.txt">Table of n, a(n) for n = 2..1000</a>

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>

%F a(n) = 10^n - floor(10^n/7) - floor(10^n/30) + floor(10^n/210).

%e a(6) = 10^6 - floor(10^6/7) - floor(10^6/30) + floor(10^6/210) = 1000000 - floor(142857.142...) - floor(33333.333...) + floor(4761.904...) = 1000000 - 142857 - 33333 + 4761 = 828571.

%p f := n->10^n-floor(10^n/7)-floor(10^n/30)+floor(10^n/210);

%o (Magma) [10^n-Floor(10^n/7)-Floor(10^n/30)+Floor(10^n/210): n in [2..20]]; // _Vincenzo Librandi_, Oct 02 2011

%K nonn

%O 2,1

%A _Milan Janjic_, Apr 28 2007

%E Example edited by _Jon E. Schoenfield_, Nov 17 2018