Note on Ramanujan's arithmetical function τ (n)

In his remarkable memoir ‘On certain arithmetical functions’* Ramanujan considers, among other functions of much interest, the. function τ(n) defined by This function is important in the theory of the representation of a number as a sum of 24 squares. In fact where r24 (n) is the number of representations; where σs(n) is the sum of the 8th powers of the divisors of n, and the sum of those of its odd divisors; and