TOPICS
Search

Arithmetic Function

An arithmetic function is a function f(n) defined for all n in N, usually taken to be complex-valued, so that f:N->C (Jones and Jones 1998, p. 143).

An alternative definition of arithmetic function is a function psi(n) such that

psi(n+m)=psi(psi(n)+psi(m))

and

psi(nm)=psi(psi(n)psi(m))

(Atanassov 1985; Trott 2004, p. 28).

See also

Integer Function, Number Theoretic Function

Explore with Wolfram|Alpha

References

Atanassov, K. "An Arithmetic Function and Some of Its Applications." Bull. Number Th. Related Topics 9, 18-27, 1985.Jones, G. A. and Jones, J. M. "Arithmetic Functions." Ch. 8 in Elementary Number Theory. Berlin: Springer-Verlag, pp. 143-162, 1998.Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, 2004. http://www.mathematicaguidebooks.org/.

Referenced on Wolfram|Alpha

Arithmetic Function

Cite this as:

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

Subject classifications