"Coprimal Harmonic Numbers"

[Leroy Quet]

In,

http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?A
num=A069220

we have the denominators of the sequence:

sum{1<=k<=n,GCD(k,n)=1} 1/k.


But the EIS, curiously, does not have the numerators, nor does it have 
the sequence of the  above sum multiplied by n!.

I was looking at this old sci.math post of mine, which inspired the email 
to seq.fan.
 
http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&safe=off&threadm=b4be2fd
f.0308251538.744cc55b%40posting.google.com&rnum=9&prev=


thanks,
Leroy Quet