Ramanujan's sum
A math function by Srinivasa Ramanujan / From Wikipedia, the free encyclopedia
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Not to be confused with Ramanujan summation.
In number theory, Ramanujan's sum, usually denoted cq(n), is a function of two positive integer variables q and n defined by the formula
where (a, q) = 1 means that a only takes on values coprime to q.
Srinivasa Ramanujan mentioned the sums in a 1918 paper.[1] In addition to the expansions discussed in this article, Ramanujan's sums are used in the proof of Vinogradov's theorem that every sufficiently large odd number is the sum of three primes.[2]