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A348709 Number of squarefree integers with an even number of prime factors <= 10^n. 1

%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

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)