75th Romanian Mathematical Olympiad

a) Since $45^2=2025$, the smalls which are perfect squares are $1^2,2^2,3^2,\dots ,45^2$, that is $45$ such numbers.

b) The smalls which are perfect squares and are divisible by $45$ are $15^2,4\cdot 15^2$ and $9\cdot 15^2$ – there are $3$ of them.

c) The smalls divisible by $45$ are $45\cdot 1,45\cdot 2,\dots ,45\cdot 45$ – there are $45$ such numbers. The number of smalls which are perfect squares or are divisible by $45$ is $45+45-3=87$. So, the number of smalls which are neither perfect squares, nor leave remainder $0$ when divided by $45$ is $2025-87=1938$.