# Pillai's arithmetical function

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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]}

## References

- ↑
^{1.0}^{1.1}^{1.2}{{#invoke:Citation/CS1|citation |CitationClass=journal }} - ↑ http://math.stackexchange.com/questions/135351/sum-of-gcdk-n
- ↑ {{#invoke:Citation/CS1|citation |CitationClass=journal }}