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 A070548 #27 Feb 16 2025 08:32:46
%S A070548 1,1,1,1,1,2,2,2,2,3,3,3,3,4,5,5,5,5,5,5,6,7,7,7,7,8,8,8,8,8,8,8,9,10,
%T A070548 11,11,11,12,13,13,13,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,17,
%U A070548 18,18,18,18,19,19,19,20,20,20,20,21,21,21,21,21,22,22,22,23,23,23,23
%N A070548 a(n) = Cardinality{ k in range 1 <= k <= n such that Moebius(k) = 1 }.
%C A070548 Moebius(k)=1 iff k is the product of an even number of distinct primes (cf. A008683). See A057627 for Moebius(k)=0.
%C A070548 There was an old comment here that said a(n) was equal to A072613(n) + 1, but this is false (e.g., at n=210). - _N. J. A. Sloane_, Sep 10 2008
%H A070548 N. J. A. Sloane, <a href="/A070548/b070548.txt">Table of n, a(n) for n = 1..10000</a>
%H A070548 Ed Pegg Jr., <a href="https://web.archive.org/web/20130603144755/http://www.maa.org:80/editorial/mathgames/mathgames_11_03_03.html">The Möbius Function (and squarefree numbers)</a>, Math Games, November 3, 2003.
%H A070548 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MertensConjecture.html">Mertens Conjecture</a>.
%F A070548 Asymptotics: Let N(i) = number of k in the range [1,n] with mu(k) = i, for i = 0, 1, -1. Then we know N(1) + N(-1) ~ 6n/Pi^2 (see A059956). Also, assuming the Riemann hypothesis, | N(1) - N(-1) | < n^(1/2 + epsilon) (see the Mathworld Mertens Conjecture link). Hence a(n) = N(1) ~ 3n/Pi^2 + smaller order terms. - _Stefan Steinerberger_, Sep 10 2008
%F A070548 a(n) = (1/2)*Sum_{i=1..n} (mu(i)^2 + mu(i)) = (1/2)*(A013928(n+1) + A002321(n)). - _Ridouane Oudra_, Oct 19 2019
%F A070548 From _Amiram Eldar_, Oct 01 2023: (Start)
%F A070548 a(n) = A013928(n+1) - A070549(n).
%F A070548 a(n) = A070549(n) + A002321(n). (End)
%p A070548 with(numtheory); M:=10000; c:=0; for n from 1 to M do if mobius(n) = 1 then c:=c+1; fi; lprint(n,c); od; # _N. J. A. Sloane_, Sep 14 2008
%t A070548 a[n_] := If[MoebiusMu[n] == 1, 1, 0]; Accumulate@ Array[a, 100] (* _Amiram Eldar_, Oct 01 2023 *)
%o A070548 (PARI) for(n=1,150,print1(sum(i=1,n,if(moebius(i)-1,0,1)),","))
%Y A070548 Cf. A008683, A002321, A013928, A059956, A070549.
%K A070548 easy,nonn
%O A070548 1,6
%A A070548 _Benoit Cloitre_, May 02 2002