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A285881 Number of even squarefree numbers <= n.

%I A285881 #9 Feb 16 2025 08:33:44
%S A285881 0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,8,
%T A285881 8,8,8,9,9,9,9,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,
%U A285881 12,12,13,13,13,13,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,17,18,18,18,18
%N A285881 Number of even squarefree numbers <= n.
%H A285881 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squarefree.html">Squarefree</a>
%F A285881 G.f.: Sum_{k>=1} x^A039956(k)/(1 - x).
%F A285881 a(n) ~ 2*n/Pi^2.
%t A285881 Table[Sum[Boole[EvenQ[k] && SquareFreeQ[k]], {k, 1, n}], {n, 85}]
%t A285881 nmax = 85; Rest[CoefficientList[Series[Sum[Boole[EvenQ[k] && MoebiusMu[k]^2 == 1] x^k/(1 - x), {k, 1, nmax}], {x, 0, nmax}], x]]
%o A285881 (Python)
%o A285881 from sympy.ntheory.factor_ import core
%o A285881 def a(n): return sum([1 for k in range(1, n + 1) if k%2==0 and core(k)==k]) # _Indranil Ghosh_, Apr 28 2017
%Y A285881 Cf. A005117, A008683, A013928, A039956, A285879.
%K A285881 nonn
%O A285881 1,6
%A A285881 _Ilya Gutkovskiy_, Apr 27 2017