A348708 Number of squarefree integers with an odd number of prime factors <= 10^n.

0, 4, 30, 303, 3053, 30421, 303857, 3039127, 30395383, 303963673, 3039652332, 30396399068, 303963519954, 3039635209356, 30396355530761, 303963552535238, 3039635510867921, 30396355103617024, 303963550950390745, 3039635508820145344, 30396355092470750098, 303963550928711270447

Offset: 0

Author

Giorgos Kalogeropoulos, Oct 30 2021

Keywords

• nonn

Comments

a(n) is the number of integers k <= 10^n with mu(k)=-1 where mu(k) is the Möbius function.

Examples

			a(1) = 4 because there are 4 squarefree integers with an odd number of prime factors <= 10: 2, 3, 5, 7.
		

Crossrefs

Cf. A071172, A084237, A008683, A030059, A104141, A348709.

Programs

Mathematica

Table[Length@Select[Range[10^n],MoebiusMu@#==-1&],{n,0,6}]

Formula

a(n) = (A071172(n) - A084237(n)) / 2.

Lim_{n->oo} a(n)/10^n = 3/Pi^2 (A104141).