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 A285879 #25 Feb 16 2025 08:33:44
%S A285879 1,1,2,2,3,3,4,4,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,11,11,11,11,12,
%T A285879 12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,19,19,20,20,20,20,21,21,
%U A285879 22,22,23,23,24,24,25,25,26,26,26,26,27,27,28,28,29,29,30,30,31,31,31,31,32,32,33,33,33,33,34,34,35
%N A285879 Number of odd squarefree numbers <= n.
%H A285879 Robert Israel, <a href="/A285879/b285879.txt">Table of n, a(n) for n = 1..10000</a>
%H A285879 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squarefree.html">Squarefree</a>
%F A285879 G.f.: Sum_{k>=1} x^A056911(k)/(1 - x).
%F A285879 a(n) ~ 4*n/Pi^2. See A185199.
%F A285879 a(n) = Sum_{k=1..n} A008683(2k)^2. - _Ridouane Oudra_, Aug 16 2019
%p A285879 ListTools:-PartialSums(map(op,[seq(`if`(numtheory:-issqrfree(n),[1,0],[0,0]),n=1..100,2)])); # _Robert Israel_, May 07 2018
%p A285879 seq(add(mobius(2*k)^2, k=1..n), n=1..100); # _Ridouane Oudra_, Aug 16 2019
%t A285879 Table[Sum[Boole[OddQ[k] && SquareFreeQ[k]], {k, 1, n}], {n, 85}]
%t A285879 nmax = 85; Rest[CoefficientList[Series[Sum[Boole[OddQ[k] && MoebiusMu[k]^2 == 1] x^k/(1 - x), {k, 1, nmax}], {x, 0, nmax}], x]]
%o A285879 (PARI) a(n) = sum(k=1, n, (k%2)*issquarefree(k)); \\ _Michel Marcus_, Apr 27 2017
%o A285879 (Python)
%o A285879 from sympy.ntheory.factor_ import core
%o A285879 def a(n): return sum([1 for k in range(1, n + 1) if k%2==1 and core(k)==k]) # _Indranil Ghosh_, Apr 28 2017
%Y A285879 Cf. A005117, A008683, A013928, A056911, A185199, A285881.
%K A285879 nonn
%O A285879 1,3
%A A285879 _Ilya Gutkovskiy_, Apr 27 2017