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

1,49

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

Links

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

Formula

a(A005117(n)) = 0.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A051699.

Cf. A005117, A081221.

Sequence in context: A135929 A346377 A338757 * A080732 A301295 A215036

Adjacent sequences: A080730 A080731 A080732 * A080734 A080735 A080736

Keyword

nonn

Author

Benoit Cloitre, Mar 08 2003

Extensions

Examples added by Antti Karttunen, Sep 22 2017

Status

approved