[seqfan] Re: At least the first 6 values are the same for A002884 and for A061350(2^n)

Jonathan Post jvospost3 at gmail.com
Wed Aug 11 17:56:35 CEST 2010

Sorry.  Meant to also ask if, likewise, A053290(n) = A061350(3^n)?

A053290  	 Number of nonsingular n X n matrices over GF(3).

Additional external references would be:

 Avinoam Mann, Philip Hall’s “rather curious” formula for abelian
p-groups, Israel J. Math. 96 (1996), part B, 445-448.

Francis Clarke, Counting abelian group structures, Proceedings of the
AMS, 134 (2006), 2795–2799.

On Wed, Aug 11, 2010 at 8:50 AM, Jonathan Post <jvospost3 at gmail.com> wrote:
> Is it true (I just woke up and don't clearly recall my Group Theory)
> that  A002884  is A061350(2^n)?
> A002884         Number of nonsingular n X n matrices over GF(2) (order of
> Chevalley group A_n (2)).
> (Formerly M4302 N1798)
>        1, 1, 6, 168, 20160, 9999360, ...
> A061350         Maximal size of Aut(G) where G is a finite Abelian group of order n.
> If so, a nice comment would be  Hall's:
> "The sum of the reciprocals of the orders of all the Abelian groups of
> order a power of p is equal to the sum of the reciprocals of the
> orders of their groups of automorphisms."
> Link to:
> John Baez:
> This Week’s Finds in Mathematical Physics (Week 300)
> http://johncarlosbaez.wordpress.com/2010/08/11/this-weeks-finds-in-mathematical-physics-week-300/#comment-469
> This is the last of the old series of This Week’s Finds. Soon the new
> series will start, focused on technology and environmental issues —
> but still with a hefty helping of math, physics, and other science....
> But now… the grand finale of This Week’s Finds in Mathematical Physics!
> I’d like to take everything I’ve been discussing so far and wrap it up
> in a nice neat package. Unfortunately that’s impossible – there are
> too many loose ends. But I’ll do my best: I’ll tell you how to
> categorify the Riemann zeta function. This will give us a chance to
> visit lots of our old friends one last time: the number 24, string
> theory, zeta functions, torsors, Joyal’s theory of species,
> groupoidification, and more.

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