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]

[4]

References

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