A271774 - OEIS

%I #11 Apr 15 2016 15:57:17

%S 1,1,2,3,2,5,2,7,4,7,2,11,2,13,6,13,2,17,2,19,10,19,2,23,6,23,4,27,2,

%T 29,2,31,12,31,10,33,2,37,16,37,2,41,2,43,6,43,2,47,10,49,18,47,2,53,

%U 12,53,22,53,2,59,2,61,10,61,16,61,2,67,26,67,2,71,2

%N a(1) = 1, then a(n) is the maximum of all 0 < m < n for which a(m) divides n.

%C If n is an odd prime, then a(n) = 2 and a(n+1) = n.  All n for which a(n) = 2 are odd primes. - _Robert Israel_, Apr 14 2016

%H Robert Israel, <a href="/A271774/b271774.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 1 by definition.

%e a(2) = 1 because a(1) divides 2.

%e a(3) = 2 because a(2) divides 3.

%e a(4) = 3 because a(3) divides 4.

%e a(5) = 2 because a(2) divides 5.

%e a(6) = 5 because a(5) divides 6.

%e a(7) = 2 because a(2) divides 7.

%e a(8) = 7 because a(7) divides 8.

%p A:= proc(n) option remember; local m;

%p     for m from n-1 by -1 do

%p       if n mod A(m) = 0 then return m fi

%p     od

%p end proc:

%p A(1):= 1:

%p seq(A(i),i=1..100); # _Robert Israel_, Apr 14 2016

%t a[1] = 1; a[n_] := a[n] = Block[{m = n - 1}, While[Mod[n, a[m]] > 0, m--]; m]; Array[a, 100] (* _Giovanni Resta_, Apr 14 2016 *)

%Y Cf. A088167, A269347, A271503, A271504, A271773.

%K nonn

%O 1,3

%A _Peter Kagey_, Apr 14 2016