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

Author

Franklin T. Adams-Watters, Jan 25 2018

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

PARI

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