tau.m

Given a nonnegative integer n, tau(n) is the Ramanujan tau function of n.

Given a nonnegative integer n, tau(n) is the Ramanujan tau function of n, defined as the coefficient of x^n in the Taylor expansion of
x * prod_{k>=0}(1 - x^k)^24. This is an integer function with fascinating number theoretic properties. For instance, it's multiplicative, meaning tau(m*n) = tau(m)*tau(n) for m and n coprime. It also satisfies some unusual modular properties, like
tau(n) - sigma_11(n) is always divisible by 691. It's also important in the study of elliptic curves and modular forms.