(phi(m)+1) divides m

[Leroy Quet]

Let phi(m) 
be the number of positive integers <= m and relatively prime with m.

I get, by hand, that the sequence of m's where

(phi(m)+1)|m

begins

2, 3, 5, 6, 7, 10, 11, 13, 14, 17, 19,..

(Not in the EIS, apparently.)

What can be said about this sequence, such as its asymptotics, the best 
way to determine if an integer is in it, etc ?

Although this sequence's definition seems unnatural, I was wondering 
about it because
phi(p) = p-1, if p = a prime.

thanks,
Leroy Quet