A multiplicative function is a number theoretic function such that, for all positive integers and , (i.e., the statement that and are relatively prime) implies

(Wilf 1994, p. 58).

Examples of multiplicative functions are the Möbius function and totient function.

See also

Completely Multiplicative Function, Möbius Function, Multiplicative Number Theoretic Function, Quadratic Residue, Sárközy Local Extrema Conjectures, Totient Function

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References

Wilf, H. S. Generatingfunctionology, 2nd ed. New York: Academic Press, 1994.

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Multiplicative Function

Cite this as:

Weisstein, Eric W. "Multiplicative Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MultiplicativeFunction.html

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