(phi(m)+1) divides m

[Jim Nastos]

On Thu, 15 Apr 2004, Leroy Quet wrote:

> 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 ?

  After looking at this sequence up to 1000, it looks as though this 
sequence is exactly the set of primes union all 2p, for p an odd prime.

  It is easy to see that all primes and the 2p numbers must all belong to 
this sequence, but I don't immediately see why these are the only numbers 
(it's not hard to see that these are the only numbers with at most two 
prime divisors, though.)

J

P.S. Here is a sequence extension of the above:
(17, 19,) 22, 23, 26, 29, 31, 34, 37, 38, 41, 43, 46, 47, 53, 58, 59, 61, 
62, 67, 71, 73, 74, 79, 82, 83, 86, 89, 94, 97, 101, 103, 106, 107, 109, 
113, 118, ...