A298734 a(n) = n-th term in periodic sequence repeating the divisors of n in decreasing order.

1, 1, 3, 4, 5, 3, 7, 1, 1, 5, 11, 1, 13, 7, 3, 16, 17, 1, 19, 10, 21, 11, 23, 1, 25, 13, 3, 4, 29, 3, 31, 16, 33, 17, 5, 1, 37, 19, 3, 1, 41, 21, 43, 22, 9, 23, 47, 3, 49, 25, 3, 4, 53, 3, 5, 1, 57, 29, 59, 1, 61, 31, 9, 64, 65, 33, 67, 34, 69, 5, 71, 1, 73, 37, 15, 4, 77, 3, 79, 1, 81, 41, 83, 1, 85, 43, 3, 1, 89, 10, 7, 46, 93, 47

Offset

1,3

Links

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

Example

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

Maple

with(numtheory):
a:= n-> 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

Table[PadRight[{}, n, Reverse[Divisors[n]]][[-1]], {n, 100}] (* Harvey P. Dale, Jul 21 2024 *)

Prog

(PARI) a(n) = my(d=Vecrev(divisors(n))); if (n % #d, d[n % #d], 1); \\ Michel Marcus, Jan 26 2018

Crossrefs

Cf. A122377 (n/a(n)), A033950 (indices of 1's).

Sequence in context: A330740 A178231 A343262 * A137926 A218342 A090395

Adjacent sequences: A298731 A298732 A298733 * A298735 A298736 A298737

Keyword

nonn

Author

Franklin T. Adams-Watters, Jan 25 2018

Status

approved