A160764 a(n) = n-th squarefree number minus round(n*zeta(2)).

-1, -1, -2, -2, -2, -3, -2, -2, -2, -2, -3, -3, -2, -2, -3, -3, -2, -1, -1, -2, -2, -2, -3, -2, -3, -4, -3, -4, -5, -3, -4, -2, -1, -1, -1, -1, -2, -2, -2, -1, -1, -2, -2, -2, -3, -3, -3, -2, -3, -3, -2, -3, -2, -3, -3, -3, -3, -2, -3, -4, -3, -1, -2, -2, -2, -3, -3, -3, -4

Offset: 1

Author

Daniel Forgues, May 26 2009

Keywords

• sign

Comments

Race between the n-th squarefree number and round(n*zeta(2)).

Links

• Daniel Forgues, Table of n, a(n) for n=1..60794

Crossrefs

Cf. A005117 Squarefree numbers.

Cf. A013929 Nonsquarefree numbers.

Cf. A013928 Number of squarefree numbers < n.

Cf. A158819 Number of squarefree numbers <= n minus round(n/zeta(2)).

Formula

Since zeta(2) = Sum_{i>=1}, 1/(i^2) = (Pi^2)/6, we get:

a(n) = A005117(n) - n * Sum_{i>=1}, 1/(i^2) = O(sqrt(n));

a(n) = A005117(n) - n * (Pi^2)/6 = O(sqrt(n)).