Sequence: (m-k) divides a(m)*a(k)

[Leroy Quet]

[Posted also to sci.math.]

Here is a sequence similar to the one I describe in the message
"Indexes' Difference Divides Sum Of 2 Terms",

But here I multiply adjacent terms instead of add them.

Let a(1)  = 1; 

Let a(m) = lowest positive unpicked integers such that:

(m-k) divides evenly into (a(m) * a(k))

for EACH k, 1 <= k <= m-1.


I get (again, figured by hand, so not completely believable):

a(m) : 1, 2, 4, 3, 12, 30,...

Now this looks less like it might be a permutation of the positive 
integers, less likely a permutation than the sequence in the link above, 
in any case.

Is it a permutation of the positive integers?

thanks,
Leroy Quet