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Completely Multiplicative Function

A completely multiplicative function, sometimes known as linear or totally multiplicative function, is an arithmetic function f(n) such that

f(mn)=f(m)f(n)

holds for each pair of positive integers (m,n).

See also

Hall-Montgomery Constant, Multiplicative Function

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References

Apostol, T. M. "Some Properties of Completely Multiplicative Arithmetical Functions." Amer. Math. Monthly 78, 266-271, 1971.Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, p. 206, 2003.Haukkanen, P. "On Characterizations of Completely Multiplicative Arithmetical Functions." Number Theory (Turku, 1999). Berlin: de Gruyter, Berlin, pp. 115-123, 2001.Kátai, I. and Kovács, B. "Multiplicative Functions with Nearly Integer Values." Acta Sci. Math. 48, 221-225, 1985.Laohakosol, V. and Pabhapote, N. "Completely Multiplicative Functions Arising from Simple Operations." Int. J. Math. Math. Sci., No. 9-12, 431-441, 2004.Sivaramakrishnan, R. Classical Theory of Arithmetic Functions. New York: Dekker, 1989.McCarthy, P. J. Introduction to Arithmetical Functions. New York: Springer-Verlag, 1986.Vaidyanathaswamy, R. "The Theory of Multiplicative Arithmetic Functions." Trans. Amer. Math. Soc. 33, 579-662, 1931.

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Completely Multiplicative Function

Cite this as:

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

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