[SeqFan] pi(x) divides x

[Jud McCranie]

A consequence of the prime number theorem is that for any positive integer
n, there is an x such that x >= n*pi(x).  I was wondering about solutions
of x=n*pi(x).  I just submitted sequence A038625, which gives the smallest
value of x such that x = n*pi(x) for n = 2, 3, ... 23.  A038626 gives the
corresponding values of pi(x) and A038627 gives the number of solutions for
n = 2, 3, ... 23.  At one extreme, n=11 has only one solution; at the other
extreme, n=18 has 33 solutions.

This is just a curiosity, but does anyone have any idea if solutions of
x=n*pi(x) exist for all n>1?  
+--------------------------------------------------------------------+
| Jud McCranie    jud.mccranie at mindspring.com  or   @camcat.com      |
|                                                                    |
| "We should regard the digital computer system as an instrument to  |
| assist the number theorist in investigating the properties of his  |
| universe - the natural numbers."  D. H. Lehmer, 1974 (paraphrased) |
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