Ramanujan's Sum - Notation

Notation

For integers a and b, is read "a divides b" and means that there is an integer c such that b = ac. Similarly, is read "a does not divide b". The summation symbol means that d goes through all the positive divisors of m, e.g.

\sum_{d\,\mid\,12}f(d) =
f(1) + f(2) + f(3) + f(4) + f(6) + f(12).

is the greatest common divisor,

is Euler's totient function,

is the Möbius function, and

is the Riemann zeta function.

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