login
A348709
Number of squarefree integers with an even number of prime factors <= 10^n.
1
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved