“Pillai's arithmetical function”的意思、由来-开放百科全书

词条

Pillai's arithmetical function

释义

References

In number theory, the gcd-sum function,^[1]

also called Pillai's arithmetical function,^[1] is defined for every by

or equivalently^[1]

where is a divisor of and is Euler's totient function.

it also can be written as^[2]

where, is the Divisor function, and is the Möbius function.

This multiplicative arithmetical function was introduced by the Indian mathematician Subbayya Sivasankaranarayana Pillai in 1933.^[3]

^[4]

References

1. ^¹²{{cite journal |author=Lászlo Tóth |title=A survey of gcd-sum functions |journal=J. Integer Sequences |volume=13 |year=2010}}
2. ^http://math.stackexchange.com/questions/135351/sum-of-gcdk-n
3. ^{{cite journal |author=S. S. Pillai |title=On an arithmetic function |journal=Annamalai University Journal |volume=II |year=1933 |pages=242–248}}
4. ^{{cite journal |last1=Broughan |first1=Kevin |title=The gcd-sum function |journal=Journal of Integer Sequences |date=2002 |volume=4 |issue=Article 01.2.2 |pages=1-19 }}

1 : Arithmetic functions

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。