This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

RamanujanTau

 RamanujanTau[n] gives the Ramanujan function .
• Integer mathematical function.
• gives the coefficient of in the series expansion of .
The first 10 values of RamanujanTau:
The first 10 values of RamanujanTau:
 Out[1]=
 Scope   (4)
Evaluate RamanujanTau for large arguments:
RamanujanTau is zero for all non-positive integers:
 Applications   (6)
Logarithmic plot of RamanujanTau:
The first prime value of RamanujanTau:
The first 20,000 values are nonzero, satisfying Lehmer's conjecture []:
Plot of at primes :
The modular discriminant:
Relation with DedekindEta:
The summatory -function []:
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:
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