Add to n its second smallest non-divider. Loop

[franktaw at netscape.net]

This rule simply takes n to 2n + tau(n).

Franklin T. Adams-Watters

-----Original Message-----
From: Eric Angelini <Eric.Angelini at kntv.be>

Could please someone compute a few terms more of:

< Add to n the n-th smallest number not dividing n >

(this is a kind of self-generalization of the rule herunder)

I've found this first few terms:

S = 1,3,8,20,46,96,...

Best,
É.

(not in the OEIS though 1,3,8,20,46 gives 4 hits)