A037228: pi - phi

[franktaw at netscape.net]

 A037228 is incorrectly named; the sequence is actually phi(n)-pi(n), not pi(n)-phi(n).  The comment is then correct (based on A037229); a(90) = 0.
 
Incidently, this is an example of two adjacent, closely related sequences with different authors.  (Apropos the discussion a while back about the value of the "Adjacent Sequences" line.)
 
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645
 
 
-----Original Message-----
From: Alonso Del Arte <alonso.delarte at gmail.com>
To: seqfan at ext.jussieu.fr
Sent: Mon, 3 Oct 2005 13:38:40 -0400
Subject: A037228: pi - phi


I'm a little confused about the comment for A037228, I'm wondering if
I'm reading it wrong (I might be getting confused about the direction
of greater than and less than signs). It says: "It is known that a(n)
>= 0 for n >= 61." For example, pi(61) - phi(61) = -42, which is
clearly less than zero. But pi(62) - phi(62) = -12. In fact, the
Mathematica command

Select[Range[10000], (PrimePi[#] - EulerPhi[#]) < 0 &]

gives you almost all the first 10000 integers. The skipped integers
are {2, 3, 4, 6, 8, 10, 12, 14, 18, 20, 24, 30, 42, 60, 90} (listed in
A037229).

Alonso
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