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
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