%I #15 Nov 09 2021 06:41:33
%S 1,3,31,305,3030,30373,304069,3040164,30397311,303963451,3039618610,
%T 30396311212,303963582320,3039635808938,30396354655186,
%U 303963549318865,3039635507672484,30396355081786770,303963550903632005,3039635509720135531,30396355092931863204,303963550925315375170
%N Number of squarefree integers with an even number of prime factors <= 10^n.
%C a(n) is the number of integers k <= 10^n with mu(k)=1 where mu(k) is the Möbius function.
%F a(n) = (A071172(n) + A084237(n)) / 2.
%F Lim_{n->oo} a(n)/10^n = 3/Pi^2 (A104141).
%e a(1) = 3 because there are 3 squarefree integers with an even number of prime factors <= 10: 1, 6, 10.
%t Table[Length@Select[Range[10^n],MoebiusMu@#==1&],{n,0,6}]
%Y Cf. A071172, A084237, A008683, A030229, A104141, A348708.
%K nonn
%O 0,2
%A _Giorgos Kalogeropoulos_, Oct 30 2021
|