Equations 20 & 21 of Riemann's Zeta Function at Mathworld.

What intrigues me about these equations is the apparent lack of any

symmetry, which is why I was fairly gobsmacked when sigma(n>0,omega(n)/n^2)

was zeta(zeta(2)*2)/zeta(zeta(2)).

P.S. I (or Proth to be more precise - using a NewPGen sieve), determined

that 4472*1001^567+1 is prime. Do I win a prize?

Jon Perry

perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript

http://www.brainbench.com
-----Original Message-----

From: djbroadhurst [mailto:

d.broadhurst@...]

Sent: 01 July 2002 10:29

To:

primenumbers@yahoogroups.com
Subject: [PrimeNumbers] Re: Almost amazing fact

I said to Jon Perry:

> If you want to generate exact old truths,

> instead of approximate new nonsense,

> use bigomega.

But I've just recalled a

truly amazing littleomega fact:

sum(n>0,2^omega(n)/n^(2*k))

is _rational_ for all integers k>0.

(It's 90/6^2=5/2 at k=1 and in general

zeta(2*k)^2/zeta(4*k))

David

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