JMO 1993 Problem 2

Denote by $d(n)$ the largest odd divisor of positive integers $n$ and define $D(n),\ T(n)$ as follows. $$D(n)=d(1)+d(2)+\cdots +d(n),\ \ T(n)=1+2+\cdots +n.$$

Prove that there existed infinitely positive integers $n$ such that $3D(n)=2T(n).$