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</math>
for all positive integers <math>m, n</math> with <math>(m, n)=1</math>.
It is easy to see that an arithmetical function <math>f</math> not identically zero is quasimultiplicative if and only if <math>f(1)\ne 0</math> and
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for all <math>m, n</math> with <math>(m, n)=1</math>. Then <math>c=f(1)</math>.
Quasimultiplicative functions are multiplicative functions
multiplied by a (nonzero) constant.
An arithmetical function <math>f</math> not identically zero is quasimultiplicative if and only if <math>f(1)\ne 0</math> and <math>f/f(1)</math> is multiplicative.
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A nice characterization is as follows.
An arithmetical function <math>f</math> (not identically zero) is semimultiplicative if and only if
<math>
f(m)f(n)=f((m, n))f([m, n])
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\left(\frac{f(ap^{\nu_p(n)-\nu_p(a)})}{f(a)}\right).
</math>
Note that some authors define that the function identically zero is multiplicative and thus quasimultiplicative etc.
==See also==
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