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

1, 3, 31, 305, 3030, 30373, 304069, 3040164, 30397311, 303963451, 3039618610, 30396311212, 303963582320, 3039635808938, 30396354655186, 303963549318865, 3039635507672484, 30396355081786770, 303963550903632005, 3039635509720135531, 30396355092931863204, 303963550925315375170

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..21.

Formula

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

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

Example

a(1) = 3 because there are 3 squarefree integers with an even number of prime factors <= 10: 1, 6, 10.

Mathematica

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

Crossrefs

Cf. A071172, A084237, A008683, A030229, A104141, A348708.

Sequence in context: A236957 A112425 A144579 * A220997 A222094 A069589

Adjacent sequences: A348706 A348707 A348708 * A348710 A348711 A348712

Keyword

nonn

Author

Giorgos Kalogeropoulos, Oct 30 2021

Status

approved