Jordan's totient function
- Jordan's totient function
In number theory, Jordan's totient function of a positive integer "n" is the number of "k"-tuples of positive integers all less than or equal to "n" that form a coprime ("k" + 1)-tuple together with "n". This is a generalisation of Euler's totient function, which is "J"1. The function is named after Camille Jordan.
Definition
Jordan's totient function is multiplicative and may be evaluated as
:
Properties
*
* The average order of "J""k"("n") is "c" "n""k" for some "c".
References
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*cite book | title=Problems in Analytic Number Theory | author=M. Ram Murty | authorlink=M. Ram Murty | volume=206 | series=Graduate Texts in Mathematics | publisher=Springer-Verlag | year=2001 | isbn=0387951431 | page=11
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