A122377 - OEIS

%I #21 Jun 05 2022 19:17:14

%S 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,

%T 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,

%U 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

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

%C 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).

%H Alois P. Heinz, <a href="/A122377/b122377.txt">Table of n, a(n) for n = 1..20000</a>

%e 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.

%p with(numtheory):

%p a:= 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 f[n_] := Block[{d = Divisors[n]}, d[[Mod[n, Length[d], 1]]]];Table[f[n], {n, 100}] (* _Ray Chandler_, Oct 26 2006 *)

%t Table[PadRight[{},n,Divisors[n]][[-1]],{n,100}] (* _Harvey P. Dale_, Jun 05 2022 *)

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

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

%Y Cf. A033950 (fixed points). [From _Franklin T. Adams-Watters_, Jul 11 2009]

%K nonn

%O 1,2

%A _Leroy Quet_, Oct 19 2006

%E Edited and extended by _Ray Chandler_, Oct 26 2006

%E New name from _Franklin T. Adams-Watters_, Jan 25 2018