[seqfan] Re: Intermediate result for ordering problem: 2-D \phi()

[David Wilson]

Yes, your sum is prettier.

Does it actually define the same function though?

Doesn't it force you to extend the function to non-positive arguments?

----- Original Message ----- 
From: <hv at crypt.org>
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Cc: <njas at research.att.com>
Sent: Sunday, November 30, 2008 3:13 AM
Subject: [seqfan] Re: Intermediate result for ordering problem: 2-D \phi()


> That's very nice. Though it makes the computation less obvious, I'd rather
> express it as:
>
>  mn = sum_{k=1}^\inf { a([m/k], [n/k]) }
>
> .. in which each component of the sum counts the pairs with gcd equal to k
> (and analogously for higher dimension).
>
> Hugo