A285881 - OEIS

%I #8 Dec 07 2019 12:18:29

%S 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 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 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 Number of even squarefree numbers <= n.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>

%F G.f.: Sum_{k>=1} x^A039956(k)/(1 - x).

%F a(n) ~ 2*n/Pi^2.

%t Table[Sum[Boole[EvenQ[k] && SquareFreeQ[k]], {k, 1, n}], {n, 85}]

%t 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 (Python)

%o from sympy.ntheory.factor_ import core

%o 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 Cf. A005117, A008683, A013928, A039956, A285879.

%K nonn

%O 1,6

%A _Ilya Gutkovskiy_, Apr 27 2017