KöMaL 2005 B3810

Denote the greatest odd divisor of the positive integer $n$ by $k$($n$). Let $A$($n$)=$k$(1)+$k$(2)+...+$k$($n$), $B$($n$)=1+2+...+$n$. Prove that there are infinitely many values of $n$ such that 3 $A$($n$) = 2$B$($n$).