# RamanujanTau

RamanujanTau[n]

gives the Ramanujan function .

# Details • Integer mathematical function.
• gives the coefficient of in the series expansion of .
• RamanujanTau automatically threads over lists.

# Examples

open allclose all

## Basic Examples(2)

The first 10 values of RamanujanTau:

Plot over a subset of the reals:

## Scope(11)

### Numerical Evaluation(2)

Evaluate numerically:

Evaluate efficiently for large values of the argument:

### Specific Values(2)

Values at fixed points:

Value at zero:

### Visualization(3)

Plot the RamanujanTau function:

Plot the contours of the RamanujanTau function:

Plot the RamanujanTau function in three dimensions:

### Function Properties(4)

RamanujanTau is only defined for integer inputs:

RamanujanTauL is everywhere singular:

## Applications(7)

Logarithmic plot of RamanujanTau:

The first prime value of RamanujanTau:

Plot of at primes :

The modular discriminant:

Relation with DedekindEta:

The summatory -function [more info]:

The modular discriminant:

Relation with DedekindEta:

## Properties & Relations(7)

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:

FindSequenceFunction can recognize the RamanujanTau sequence:

## Possible Issues(1)

Large prime numbers can take a long time:

## Neat Examples(3)

Successive differences of RamanujanTau modulo 3:

A representation of zero in terms of RamanujanTau:

Find digit counts for RamanujanTau[10^12]: