A070544 Number of squarefree numbers s such that n < s < 2n.

0, 1, 1, 3, 2, 3, 3, 5, 6, 6, 6, 8, 7, 7, 7, 9, 9, 11, 11, 13, 13, 14, 13, 15, 15, 15, 16, 17, 17, 18, 18, 19, 19, 20, 20, 22, 22, 22, 22, 24, 23, 24, 24, 26, 27, 27, 27, 29, 30, 30, 30, 32, 32, 34, 34, 36, 36, 37, 36, 38, 37, 38, 38, 39, 39, 40, 40, 41, 41, 42, 42, 44, 44, 44, 45

Offset

1,4

Comments

Lim_{n -> infinity} a(n)/n = 6/Pi^2.

Links

Table of n, a(n) for n=1..75.

Formula

From Wesley Ivan Hurt, Jan 08 2022: (Start)

a(n) = Sum_{k=1..n-1} mu(2n-k)^2.

a(n) = Sum_{k=n+1..2n-1} mu(k)^2.

a(n) = Sum_{k=(n^2-n+2)/2..(n^2+n-2)/2} mu(A128076(k))^2. (End)

Mathematica

Table[Count[Range[n+1, 2n-1], _?SquareFreeQ], {n, 80}] (* Harvey P. Dale, Mar 23 2019 *)

Prog

(PARI) for(n=1, 100, print1(sum(i=n+1, 2*n-1, issquarefree(i)), ", "))

Crossrefs

Cf. A008966, A128076.

Sequence in context: A181672 A125748 A058680 * A087713 A089319 A140396

Adjacent sequences: A070541 A070542 A070543 * A070545 A070546 A070547

Keyword

easy,nonn

Author

Benoit Cloitre, May 02 2002

Status

approved