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A280171
a(n) is the least positive number whose divisors have all possible residues mod n.
2
1, 2, 6, 12, 40, 30, 84, 120, 288, 270, 990, 420, 936, 1638, 840, 2160, 5100, 4410, 8208, 5940, 3360, 6930, 12420, 10920, 14400, 19890, 28080, 27300, 48720, 43890, 37200, 73440, 84480, 151470, 97440, 107100, 139860, 139650, 120120, 83160, 196800, 395850, 216720, 318780, 191520, 217350, 118440, 546000, 282240, 1222650
OFFSET
1,2
COMMENTS
a(n) <= n!
A000203(a(n)) >= n.
a(n) is divisible by n.
LINKS
EXAMPLE
a(4) = 12: the divisors of 12 include 4, 1, 2, 3 == 0, 1, 2, 3 (mod 4).
a(5) = 40: the divisors of 40 include 5, 1, 2, 8, 4 == 0, 1, 2, 3, 4 (mod 5).
MAPLE
A[1]:= 1:
for k from 2 to 10^6 do
V:= numtheory:-divisors(k);
for m from 2 to nops(V) do
if not(assigned(A[m])) and (map(`modp`, V, m) = {$0..m-1}) then
A[m]:= k
fi
od
od:
seq(A(n), n=1..49);
MATHEMATICA
a[n_] := a[n] = If[n == 1, 1, For[k = n, True, k += n, If[Union[Mod[Divisors[k], n]] == Range[0, n-1], Return[k]]]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 27 2025 *)
PROG
(PARI) a(n) = my(k=1); while (#Set(apply(x->Mod(x, n), divisors(k))) != n, k++); k; \\ Michel Marcus, Jan 27 2025
CROSSREFS
Cf. A000203.
Sequence in context: A162589 A225957 A123045 * A327879 A094261 A080497
KEYWORD
nonn
AUTHOR
Robert Israel, Dec 27 2016
STATUS
approved