[seqfan] a(n) divides a(a(n))

[Eric Angelini]

Hello SeqFans,
T is the lexicographically first seq where:

a(n) divides a(a(n))
a(n) is not equal to a(a(n))

T was always extended with the smallest 
integer not yet in T and not leading to a
contradiction.

T= 2,4,1,8,6,12,9,16,18,11,22,24,14,28,
17,32,34,36,20,40,23,44,46,48,26,52,
29,56,58,31,62,64,35,68,70,72,38,76,
41,80,82,43,86,88,47,92,94,96,...

Example:
2 divides the 2nd term of T (2 d 4)
4 divides the 4th term of T (4 d 8)
1 divides the 1st term of T (1 d 3)
8 divides the 8th term of T (8 d 16)
6 divides the 6th term of T (6 d 12)
12 divides the 12th term of T (12 d 24)
...
Why is 9 the next term?
It cannot be 3 as 3 doesn't divide the 3rd term;
it cannot be 5 as 5 doesn't divide the 5th term;
it cannot be 7 as 7 would be both a(n) and a(a(n));
it cannot be 8 as 8 is already in T;
thus 9 is available as the 7th term of T because 9 doesn't contradict anything.

Best,
É.