  Let $d(n)$ be the divisor function. In 1916, S. Ramanujan stated but without
proof that $$\sum_{n\leq x}d^2(n)=xP(\log x)+E(x), $$ where $P(y)$ is a cubic
polynomial in $y$ and $$ E(x)=O(x^{{3\over 5}+\epsilon}), $$ where $\epsilon$
is a sufficiently small positive constant. He also stated that, assuming the
Riemann Hypothesis(RH), $$ E(x)=O(x^{{1\over 2}+\epsilon}). $$
  In 1922, B. M. Wilson proved the above result unconditionally. The direct
application of the RH would produce $$ E(x)=O(x^{1\over 2}(\log x)^5\log\log
x). $$ In 2003, K. Ramachandra and A. Sankaranarayanan proved the above result
without any assumption.
  In this paper, we shall prove $$ E(x)=O(x^{1\over 2}(\log x)^5). $$
