A122377 a(n) is the n-th term in periodic sequence repeating the divisors of n in increasing order.

1, 2, 1, 1, 1, 2, 1, 8, 9, 2, 1, 12, 1, 2, 5, 1, 1, 18, 1, 2, 1, 2, 1, 24, 1, 2, 9, 7, 1, 10, 1, 2, 1, 2, 7, 36, 1, 2, 13, 40, 1, 2, 1, 2, 5, 2, 1, 16, 1, 2, 17, 13, 1, 18, 11, 56, 1, 2, 1, 60, 1, 2, 7, 1, 1, 2, 1, 2, 1, 14, 1, 72, 1, 2, 5, 19, 1, 26, 1, 80, 1, 2, 1, 84, 1, 2, 29, 88, 1, 9, 13, 2, 1, 2

Offset: 1

Author

Leroy Quet, Oct 19 2006

Keywords

• nonn

Comments

Old name: a(n) = m-th positive divisor of n, where d(n) is number of positive divisors of n and m = d(n) if d(n)|n, else m = n mod d(n).

Examples

			The divisors of 6 are 1, 2, 3, 6; repeating that produces the sequence 1, 2, 3, 6, 1, 2, 3, 6, 1, 2, 3, 6, ...; the 6th term in that sequence is 2, so a(6) = 2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000005, A122383, A124332, A298734 (n/a(n)).

Cf. A033950 (fixed points). [From Franklin T. Adams-Watters, Jul 11 2009]

Programs

Maple

with(numtheory):
a:= n-> (l-> l[1+irem(n-1, nops(l))])(sort([divisors(n)[]])):
seq(a(n), n=1..100);  # Alois P. Heinz, Jan 29 2018

Mathematica

f[n_] := Block[{d = Divisors[n]}, d[[Mod[n, Length[d], 1]]]];Table[f[n], {n, 100}] (* Ray Chandler, Oct 26 2006 *)
Table[PadRight[{},n,Divisors[n]][[-1]],{n,100}] (* Harvey P. Dale, Jun 05 2022 *)

PARI

a(n) = my(d=divisors(n)); if (n % #d, d[n % #d], n); \\ Michel Marcus, Jan 26 2018

Extensions

Edited and extended by Ray Chandler, Oct 26 2006

New name from Franklin T. Adams-Watters, Jan 25 2018