Dedekind psi-function: Difference between revisions
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The Dedekind psi-function is an [[arithmetic function]] that sends any natural number <math>n</math> to the number: | The Dedekind psi-function is an [[arithmetic function]] that sends any natural number <math>n</math> to the number: | ||
<math>\psi(n) := n \prod \left( 1 + \frac{1}{p_i} \right)</math>. | <math>\psi(n) := n \prod \left( 1 + \frac{1}{p_i} \right)</math> | ||
where the product is over all primes <math>p_i</math> dividing <math>n</math>. | |||
==Relation with other arithmetic functions== | ==Relation with other arithmetic functions== | ||
* [[Euler phi-function]] has a similar expression to the Dedekind psi-function, except that the expression is <math>1 - (1/p_i)</math> rather than <math>1 + (1/p_i)</math>. | * [[Euler phi-function]] has a similar expression to the Dedekind psi-function, except that the expression is <math>1 - (1/p_i)</math> rather than <math>1 + (1/p_i)</math>. | ||
Latest revision as of 03:46, 29 April 2009
This article defines an arithmetic function or number-theoretic function: a function from the natural numbers to a ring (usually, the ring of integers, rational numbers, real numbers, or complex numbers).
View a complete list of arithmetic functions
Definition
The Dedekind psi-function is an arithmetic function that sends any natural number to the number:
where the product is over all primes dividing .
Relation with other arithmetic functions
- Euler phi-function has a similar expression to the Dedekind psi-function, except that the expression is rather than .
