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A053462 Number of positive squarefree integers less than 10^n.

%I A053462 #61 Jul 03 2025 18:22:05
%S A053462 0,6,61,608,6083,60794,607926,6079291,60792694,607927124,6079270942,
%T A053462 60792710280,607927102274,6079271018294,60792710185947,
%U A053462 607927101854103,6079271018540405,60792710185403794,607927101854022750,6079271018540280875,60792710185402613302
%N A053462 Number of positive squarefree integers less than 10^n.
%H A053462 Amiram Eldar, <a href="/A053462/b053462.txt">Table of n, a(n) for n = 0..36</a> (from the b-file at A071172; terms 0..20 from Charles R Greathouse IV)
%H A053462 Gérard P. Michon, <a href="http://www.numericana.com/answer/counting.htm#euler193">On the number of squarefree integers not exceeding N</a>.
%F A053462 a(n)/10^n = (6/Pi^2)*(1+o(1)), cf. A059956.
%F A053462 a(n) = A071172(n) - [n <= 1] where [] is the Iverson bracket. - _Chai Wah Wu_, Jun 01 2024
%e A053462 There are 608 squarefree integers smaller than 1000.
%t A053462 a[n_] := Module[{t=10^n-1}, Sum[MoebiusMu[k]Floor[t/k^2], {k, 1, Sqrt[t]}]]
%o A053462 (PARI) a(n)=sum(d=1,sqrtint(n=10^n-1), n\d^2*moebius(d)) \\ _Charles R Greathouse IV_, Nov 14 2012
%o A053462 (PARI) a(n)=my(s); forsquarefree(d=1,sqrtint(n=10^n-1), s += n\d[1]^2 * moebius(d)); s \\ _Charles R Greathouse IV_, Jan 08 2018
%o A053462 (Python)
%o A053462 from math import isqrt
%o A053462 from sympy import mobius
%o A053462 def A053462(n):
%o A053462     m = 10**n-1
%o A053462     return sum(mobius(k)*(m//k**2) for k in range(1, isqrt(m)+1)) # _Chai Wah Wu_, Jun 01 2024
%Y A053462 Cf. A005117, A013928.
%Y A053462 Cf. A059956, A063035.
%Y A053462 Apart from first two terms, same as A071172.
%Y A053462 Binary counterpart is A143658. - _Gerard P. Michon_, Apr 30 2009
%K A053462 nonn
%O A053462 0,2
%A A053462 _Harvey P. Dale_, Aug 01 2001
%E A053462 More terms from _Dean Hickerson_ and _Vladeta Jovovic_, Aug 06 2001
%E A053462 One more term from _Jud McCranie_, Sep 01 2005
%E A053462 a(0)=0 and a(14)-a(17) from _Gerard P. Michon_, Apr 30 2009
%E A053462 a(18)-a(20) from _Charles R Greathouse IV_, Jan 08 2018