MathDB

Let

n

be a positive integer. Suppose there are exactly

M

squarefree integers

k

such that

\left\lfloor\frac nk\right\rfloor

is odd in the set

\{ 1, 2,\ldots, n\}

. Prove

M

is odd.
An integer is squarefree if it is not divisible by any square other than

1

4