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%I #13 Jan 30 2023 19:10:17
%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)))
%o (Python)
%o from sympy import divisors
%o from itertools import count
%o def a(n):
%o d = divisors(n)
%o return next(k for k in count(1) if len(set(di%k for di in d))==len(d))
%o print([a(n) for n in range(1, 93)]) # _Michael S. Branicky_, Jan 30 2023
%K nonn
%O 1,2
%A _Franklin T. Adams-Watters_, Oct 31 2009
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