Mobius terminology

[N. J. A. Sloane]

On Mar 10 (while I was away) Emeric said:

> It seems that there is some confusion at some OEIS sequences 
> regarding the Mobius transform.
> Given a function g(n), defined on the positive integers, the 
> Mobius transform of g is 
    > f(n)=sum_{d|n} g(d) 
> and then, of course, g is the inverse Mobius transform of f.
> Not the other way around.
> The number theory books I have do mention Mobius pairs but do 
> not define the "Mobius transform".


Me:  I respectfully disagree!  In my "transforms" page, I give
this definition:


MOBIUS:=proc(a)  local b,i,d:
if whattype(a) <> list then RETURN([]); fi:
b:=[]:
for i to nops(a) do b:=[op(b), add( mob(i,d)*a[d], d=1..i)]: od:
RETURN(b);
end:

which is equivalent to 

         f(n) = sum_{d|n} mobius(n/d) g(d)

This is consistent with the standard usage that the 
K transform (for some kernel K) of a sequence {g} is the sequence {f}
given by an expression of the form

      f(n) = Sum_{i} K(n,i) g(i)

The binomial transform, for example, is

      f(n) = Sum_{i=0..n} C(n,i) g(i)


NJAS