

A167234


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


1



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, 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, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

What can we say about the asymptotic behavior of this sequence? Does it contain every integer > 2 infinitely often?
For n > 6, a(n) <= floor(n/2) + 1; but this seems to be a very crude estimate.


LINKS

Paul Tek, Table of n, a(n) for n = 1..10000


MATHEMATICA

allDiffQ[l_List] := (Length[l] == Length[DeleteDuplicates[l]]);
a[n_Integer] := Module[{ds = Divisors[n]},
Catch[Do[If[allDiffQ[Mod[#, m] & /@ ds], Throw[m]], {m, n}]]];
a /@ Range[92] (* Peter Illig, Jul 11 2018 *)


PROG

(PARI) alldiff(v)=v=vecsort(v); for(k=1, #v1, if(v[k]==v[k+1], return(0))); 1
a(n)=local(ds); ds=divisors(n); for(k=#ds, n, if(alldiff(vector(#ds, i, ds[i]%k)), return(k)))


CROSSREFS

Sequence in context: A079065 A097272 A126630 * A088043 A248376 A138796
Adjacent sequences: A167231 A167232 A167233 * A167235 A167236 A167237


KEYWORD

nonn


AUTHOR

Franklin T. AdamsWatters, Oct 31 2009


STATUS

approved



