  Towards the end of his life Ramanujan wrote a manuscript on properties of the
partition and tau functions, some parts of which remained unpublished until
very recently. Nevertheless, this manuscript gave rise to a lot of subsequent
work. In it Ramanujan considers congruences for $\tau(n)$ modulo some special
primes q. He proves for example that $\tau(n)\equiv \sum_{d|n}d^{11}({\rm
mod}691)$. He defines $t_n=1$ if $\tau(n)$ is not divisible by q and $t_n=0$
otherwise. He then typically writes: "It can be shown by transcendental methods
that $$ \sum_{k=1}^n t_k=C\int_1^n {dx\over (\log x)^{\delta}}+O({n\over (\log
n)^r}). $$ where r is any positive number" (after stating some weaker estimates
for the above sum). The number $\delta$ is a positve rational number depending
on q and for the positive number C Ramanujan usually wrote down an Euler
product.
  In this paper it is shown that Ramanujan's claim for every $r>1+\delta$ and
each of the special primes q is false. Furthermore, we correct a 1928 paper of
Geraldine Stanley who claimed to have disproved Ramanujan's claim in case q=5.
