prime signature

[Christian G.Bower]

------ Original Message ------
From: "kohmoto" <zbi74583 at boat.zero.ad.jp>
To: <seqfan at ext.jussieu.fr>
Subject: prime signature

>     Hi, Mitch
>     Here is an example of sequence which depends only on the prime signature

> but is not mutiplicative.
> 
>           
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A051707
> 
>     I want to know the formula.
>     I wish some one tell me it.
> 
>     Yasutoshi
>  
> 
ID Number: A051707
URL:       http://www.research.att.com/projects/OEIS?Anum=A051707
Sequence:  1,1,1,3,1,5,1,8,3,5,1,21,1,5,5,23,1,21,1,21
Name:      Number of factorizations of (n,n) into pairs (k,l).
Comments:  Pairs (k,l) must satisfy 0<k, 0<l; if k=1 then l=1. Definition of
              "*": (a,b)*(x,y)=(a*x,b*y); unit is (1,1).
           a(n) depends only on prime signature of n
Example:   (6,6)=(2,1)*(3,6)=(2,6)*(3,1)=(2,2)*(3,3)=(2,3)*(3*2), so
              a(6)=5.

Can you better explain the definition of this sequence?

You have the line "if k=1 then l=1", which obviously isn't true
because the example has a (2,1) and a (3,1). Did you mean
"if k=1 then l not= 1" to exclude (1,1).

Also for each prime you have the value 1, yet a prime can be factored
into (p,p) and (1,p)*(p,1).  Do you have a rule that excludes the latter?

Christian