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(Solved): If f is a multiplicative function, and if n=p1r1pkrk is the prime factorizatio of n, ...
If
f
is a multiplicative function, and if
n
=
p
1
r
1
?
?
…
p
k
r
k
?
?
is the prime factorizatio of
n
, then show that
?
d
?
n
?
?
(
d
)
f
(
d
)
=
(
1
?
f
(
p
1
?
)
)
×
?
×
(
1
?
f
(
p
k
?
)
)
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