A298734 - OEIS

%I #11 Jul 21 2024 16:19:04

%S 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,

%T 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,

%U 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

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

%H Alois P. Heinz, <a href="/A298734/b298734.txt">Table of n, a(n) for n = 1..20000</a>

%e 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.

%p with(numtheory):

%p a:= n-> n/(l-> l[1+irem(n-1, nops(l))])(sort([divisors(n)[]])):

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Jan 29 2018

%t Table[PadRight[{},n,Reverse[Divisors[n]]][[-1]],{n,100}] (* _Harvey P. Dale_, Jul 21 2024 *)

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

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

%K nonn

%O 1,3

%A _Franklin T. Adams-Watters_, Jan 25 2018