A076260 - OEIS

%I #24 Nov 26 2017 19:33:38

%S 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,

%T 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,

%U 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

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

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

%H Antti Karttunen, <a href="/A076260/b076260.txt">Table of n, a(n) for n = 1..16384</a>

%e 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

%t 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 *)

%o (PARI)

%o A067535(n) = { while(!issquarefree(n), n++); n; } \\ These two functions from _Michel Marcus_, Mar 18 2017

%o A070321(n) = { while(!issquarefree(n), n--); n; }

%o A076260(n) = (A067535(n)-A070321(n)); \\ _Antti Karttunen_, Nov 22 2017

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

%K nonn

%O 1,4

%A _Reinhard Zumkeller_, Oct 03 2002

%E Definition corrected to match with the data as the old definition was that of A080733 - _Antti Karttunen_, Nov 23 2017