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

1,2

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).

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

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

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

Sequence in context: A330742 A104308 A175456 * A293900 A284463 A169758

Adjacent sequences: A122374 A122375 A122376 * A122378 A122379 A122380

Keyword

nonn

Author

Leroy Quet, Oct 19 2006

Extensions

Edited and extended by Ray Chandler, Oct 26 2006

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

Status

approved