This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A071172 #75 Jul 01 2025 19:20:08
%S A071172 1,7,61,608,6083,60794,607926,6079291,60792694,607927124,6079270942,
%T A071172 60792710280,607927102274,6079271018294,60792710185947,
%U A071172 607927101854103,6079271018540405,60792710185403794,607927101854022750,6079271018540280875,60792710185402613302,607927101854026645617
%N A071172 Number of squarefree integers <= 10^n.
%C A071172 The limit of a(n)/10^n is 6/Pi^2 (see A059956). - _Gerard P. Michon_, Apr 30 2009
%H A071172 J. Pawlewicz, <a href="/A071172/b071172.txt">Table of n, a(n) for n = 0..36</a>
%H A071172 W. Hürlimann, <a href="http://dx.doi.org/10.12988/pms.2014.4615">A First Digit Theorem for Square-Free Integer Powers</a>, Pure Mathematical Sciences, Vol. 3, 2014, no. 3, 129 - 139 HIKARI Ltd.
%H A071172 G. P. Michon, <a href="http://www.numericana.com/answer/counting.htm#euler193">On the number of squarefree integers not exceeding N</a>. - _Gerard P. Michon_, Apr 30 2009
%H A071172 J. Pawlewicz, <a href="http://arxiv.org/abs/1107.4890">Counting square-free numbers</a>, arXiv preprint arXiv:1107.4890 [math.NT], 2011.
%H A071172 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squarefree.html">Squarefree</a>
%F A071172 a(n) = Sum_{i=1..10^(n/2)} A008683(i)*floor(10^n/i^2). - _Gerard P. Michon_, Apr 30 2009
%t A071172 f[n_] := Sum[ MoebiusMu[i]Floor[n/i^2], {i, Sqrt@ n}]; Table[ f[10^n], {n, 0, 14}] (* _Robert G. Wilson v_, Aug 04 2012 *)
%o A071172 (PARI) a(n)=sum(d=1,sqrtint(n=10^n),moebius(d)*n\d^2) \\ _Charles R Greathouse IV_, Nov 14 2012
%o A071172 (PARI) a(n)=my(s); forsquarefree(d=1,sqrtint(n=10^n), s += n\d[1]^2 * moebius(d)); s \\ _Charles R Greathouse IV_, Jan 08 2018
%o A071172 (Python)
%o A071172 from math import isqrt
%o A071172 from sympy import mobius
%o A071172 def A071172(n): return sum(mobius(k)*(10**n//k**2) for k in range(1,isqrt(10**n)+1)) # _Chai Wah Wu_, May 10 2024
%Y A071172 Cf. A005117, A013928.
%Y A071172 Apart from first two terms, same as A053462.
%Y A071172 Binary counterpart is A143658. - _Gerard P. Michon_, Apr 30 2009
%K A071172 nonn
%O A071172 0,2
%A A071172 _Robert G. Wilson v_, Jun 10 2002
%E A071172 Extended by _Eric W. Weisstein_, Sep 14 2003
%E A071172 3 more terms from _Jud McCranie_, Sep 01 2005
%E A071172 4 more terms from _Gerard P. Michon_, Apr 30 2009