A076260 a(n) = 0 if n is a squarefree number, otherwise the distance between the two nearest squarefree numbers around n: A067535(n)-A070321(n).

0, 0, 0, 2, 0, 0, 0, 3, 3, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 3, 3, 0, 3, 3, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 3, 3, 0, 0, 4, 4, 4, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 3, 3, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 3, 3, 0, 0, 0, 3, 3, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 4, 4, 4, 0, 0, 0, 2, 0

Offset

1,4

Comments

a(n)=0 iff n is squarefree; otherwise a(n) > 1.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Example

The nearest squarefree numbers surrounding 25 = 5^2 are A070321(25) = 23 and A067535(25) = 26, therefore a(25) = 26-23 = 3. - Edited by Antti Karttunen, Nov 23 2017

Mathematica

Block[{nn = 105, s}, s = Select[Range[nn + 15], SquareFreeQ]; Array[If[FreeQ[s, #], First@ Differences@ s[[# - 1 ;; #]] &@ FirstPosition[Union@ Append[s, #], #][[1]], 0] &, 105]] (* Michael De Vlieger, Nov 23 2017 *)

Prog

(PARI)
A067535(n) = { while(!issquarefree(n), n++); n; } \\ These two functions from Michel Marcus, Mar 18 2017
A070321(n) = { while(!issquarefree(n), n--); n; }
A076260(n) = (A067535(n)-A070321(n)); \\ Antti Karttunen, Nov 22 2017

Crossrefs

Cf. A005117, A020753, A020754, A076259, A080733.

Sequence in context: A275812 A280683 A171871 * A245527 A287871 A336644

Adjacent sequences: A076257 A076258 A076259 * A076261 A076262 A076263

Keyword

nonn

Author

Reinhard Zumkeller, Oct 03 2002

Extensions

Definition corrected to match with the data as the old definition was that of A080733 - Antti Karttunen, Nov 23 2017

Status

approved