The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A167234 Smallest number such that no two divisors of n are congruent modulo a(n). 2

%I

%S 1,2,3,4,3,6,4,5,5,6,3,7,5,8,8,9,3,10,4,7,8,6,3,13,7,7,5,11,3,11,4,9,

%T 7,6,8,13,5,5,7,11,3,16,4,12,13,6,3,17,5,11,9,7,3,10,7,15,5,5,3,21,7,

%U 7,11,11,7,14,4,7,7,16,3,13,5,10,13,7,8,14,4,17,7,6,3,23,9,8,5,13,3,19,8,12

%N Smallest number such that no two divisors of n are congruent modulo a(n).

%C What can we say about the asymptotic behavior of this sequence? Does it contain every integer > 2 infinitely often?

%C For n > 6, a(n) <= floor(n/2) + 1; but this seems to be a very crude estimate.

%H Paul Tek, <a href="/A167234/b167234.txt">Table of n, a(n) for n = 1..10000</a>

%t allDiffQ[l_List] := (Length[l] == Length[DeleteDuplicates[l]]);

%t a[n_Integer] := Module[{ds = Divisors[n]},

%t Catch[Do[If[allDiffQ[Mod[#, m] & /@ ds], Throw[m]], {m, n}]]];

%t a /@ Range[92] (* _Peter Illig_, Jul 11 2018 *)

%o (PARI) alldiff(v)=v=vecsort(v);for(k=1,#v-1,if(v[k]==v[k+1],return(0)));1

%o a(n)=local(ds);ds=divisors(n);for(k=#ds,n,if(alldiff(vector(#ds,i,ds[i]%k)),return(k)))

%K nonn

%O 1,2

%A _Franklin T. Adams-Watters_, Oct 31 2009

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 18:16 EST 2021. Contains 349567 sequences. (Running on oeis4.)