Built-in Mathematica Symbol

RamanujanTau

RamanujanTau[n]
gives the Ramanujan

function

.

The first 10 values of RamanujanTau:

Evaluate RamanujanTau for large arguments:

RamanujanTau threads over lists:

RamanujanTau is zero for all non-positive integers:

Traditional form:

Logarithmic plot of RamanujanTau:

The first prime value of RamanujanTau:

The first 20,000 values are nonzero, satisfying Lehmer's conjecture [more info]:

Plot of

at primes

:

The modular discriminant:

Relation with DedekindEta:

The summatory

-function [more info]:

The first 10 values of RamanujanTau using Product:

RamanujanTau is multiplicative for coprime integers:

For prime

:

Congruence relations:

Representation of an integer as the sum of 24 squares:

RamanujanTauL is the Dirichlet

-function associated with RamanujanTau:

Large prime numbers can take a long time:

Successive differences of RamanujanTau modulo 3:

A representation of zero in terms of RamanujanTau:

Find digit counts for RamanujanTau[10^12]: