A080733 Smallest distance from n to a squarefree number.

0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 2, 1, 0, 0, 0, 1, 0

Offset: 1

Author

Benoit Cloitre, Mar 08 2003

Keywords

• nonn

Comments

a(n) = min (abs(n-k) : where k runs through the squarefree numbers ).

The sequence is unbounded.

The first 0 occurs at 1, the first 1 at 4, the first 2 at 49, the first 3 at 846. - Antti Karttunen, Sep 22 2017

Examples

			For n = 3, 3 itself is a squarefree number, thus a(3) = 0.
For n = 48, 48 = 2^4 * 3 is not squarefree, 49 = 7^2 is not squarefree, but 47 is, thus a(48) = abs(48-47) = 1.
For n = 49, neither 49 = 7^2, nor 48 = 2^4 * 3 nor 50 = 2^2 * 5 is squarefree, while both 47 and 51 are, thus a(49) = abs(49-47) = abs(49-51) = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A051699.

Cf. A005117, A081221.

Programs

Mathematica

nn=110;With[{sqfr=Select[Range[nn+10],SquareFreeQ]},Flatten[Table[ Union[ Abs[ Nearest[ sqfr,n]-n]],{n,nn}]]] (* Harvey P. Dale, Jun 01 2012 *)

PARI

A080733(n) = { my(k=0); while((!issquarefree(n+k))&&(!issquarefree(n-k)),k++); k; }; \\ Antti Karttunen, Sep 22 2017

Formula

a(A005117(n)) = 0.

Extensions

Examples added by Antti Karttunen, Sep 22 2017