A179211 Number of squarefree numbers between n and 2*n (inclusive).

2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 8, 9, 8, 9, 9, 11, 11, 13, 13, 15, 15, 15, 15, 15, 16, 16, 17, 19, 19, 20, 19, 21, 21, 22, 22, 24, 23, 24, 24, 25, 25, 26, 26, 27, 28, 29, 29, 30, 30, 32, 32, 34, 34, 36, 36, 38, 38, 38, 38, 39, 39, 38, 39, 41, 41, 42, 41, 43, 43, 44, 44, 46, 45, 45

Offset: 1

Author

Reinhard Zumkeller, Jul 05 2010

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A008966, A013928, A035250, A061398, A179212, A179213, A179214.

Programs

Maple

a := n -> nops(select(issqrfree, [$n..(2*n)])):
seq(a(n), n=1..75); # Peter Luschny, Mar 02 2017

Mathematica

a[n_] := Select[Range[n, 2n], SquareFreeQ] // Length;
Array[a, 75] (* Jean-François Alcover, Jun 22 2018 *)

PARI

f(n)=my(s); forfactored(k=1,sqrtint(n), s += n\k[1]^2*moebius(k)); s
a(n)=f(2*n)-f(n-1) \\ Charles R Greathouse IV, Nov 05 2017

Formula

a(n) = Sum_{k=n..2*n} A008966(k).

a(n) > A035250(n) for n>2;

A179212(n) = a(n+1) - a(n);

a(n) = A013928(2*n+1) - A013928(n).

a(n) ~ (6/Pi^2) * n. - Amiram Eldar, Mar 03 2021