OFFSET
1,3
COMMENTS
n-1 <= a(n) <= A003418(n-1). - Robert Israel, Mar 08 2018
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
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..250 (first 125 terms from Andrew Weimholt)
EXAMPLE
a(7)=12: 12's divisors are 1,2,3,4,6,12 and
1 == 1 mod 7
2 == 2 mod 7
3 == 3 mod 7
4 == 4 mod 7
12 == 5 mod 7
6 == 6 mod 7
MAPLE
f:= proc(n) local k, T;
T:= {$1..(n-1)};
for k from n-1 do if T subset numtheory:-divisors(k) mod n then return k fi od
end proc:
map(f, [$1..50]); # Robert Israel, Mar 08 2018
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Weimholt, Jul 04 2008
STATUS
approved