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Ramanujan's sum

Function in number theory given by Srinivasa RamanujanIn number theory, Ramanujan's sum, usually denoted cq(n), is a function of two positive integer variables q and n defined by the formula cq(n)=∑1≤a≤q(a,q)=1e2πiaqn,{\displaystyle c_{q}(n)=\sum _{1\leq a\leq q \atop (a,q)=1}e^{2\pi i{\tfrac {a}{q}}n},}where (a, q) = 1 means that a only takes on values coprime to q. Srinivasa Ramanujan mentioned the sums in a 1918 paper.

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