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%I #23 Mar 10 2018 16:12:41
%S 1,1,2,6,8,30,12,60,96,270,90,420,72,1638,840,1080,300,4410,432,5940,
%T 3360,6930,540,10920,2880,19890,9360,27300,1680,43890,1200,36720,
%U 84480,151470,97440,107100,3780,139650,120120,83160,4800,395850,5040,318780,191520,217350
%N a(n) is smallest number with divisors which are congruent to 1, 2, ..., n-1 mod n.
%C n-1 <= a(n) <= A003418(n-1). - _Robert Israel_, Mar 08 2018
%C Records: 1, 2, 6, 8, 30, 60, 96, 270, 420, 1638, 4410, 5940, 6930, 10920, 19890, 27300, 43890, 84480, 151470, 395850, 546000, 1222650, 3267810, 5255250, ..., and they occur at indices: 1, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 22, 24, 26, 28, 30, 33, 34, 42, 48, 50, 54, 66, 69, 72, 75, 78, 82, 90, 96, 98, 106, 108, 126, 138, 150, 174, 180, 186, 192, 198, 210, ..., . - _Robert G. Wilson v_, Mar 09 2018
%H Robert G. Wilson v, <a href="/A140539/b140539.txt">Table of n, a(n) for n = 1..250</a> (first 125 terms from Andrew Weimholt)
%e a(7)=12: 12's divisors are 1,2,3,4,6,12 and
%e 1 == 1 mod 7
%e 2 == 2 mod 7
%e 3 == 3 mod 7
%e 4 == 4 mod 7
%e 12 == 5 mod 7
%e 6 == 6 mod 7
%p f:= proc(n) local k, T;
%p T:= {$1..(n-1)};
%p for k from n-1 do if T subset numtheory:-divisors(k) mod n then return k fi od
%p end proc:
%p map(f, [$1..50]); # _Robert Israel_, Mar 08 2018
%t f[n_] := Block[{k = 1, m = Range[n - 1], u}, While[u = Union@ Mod[Divisors@ k, n]; If[ u[[1]] == 0, u = Rest@ u]; u != m, k++]; k]; Array[f, 46] (* _Robert G. Wilson v_, Mar 08 2018 *)
%o (PARI) a(n) = {if (n == 1, return (1)); if (n == 2, return (1)); i = 2; cref = Set(vector(n-1, k, k)); while (1, cong = Set(); fordiv (i, d, if (d % n, cong = setunion(cong, Set(d % n)));); if (cong == cref, return (i)); i++;);} \\ _Michel Marcus_, Mar 08 2013
%Y Cf. A003418.
%K nonn
%O 1,3
%A _Andrew Weimholt_, Jul 04 2008
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