MathDB

For every natural number

a

and

b

, define the notation

[a,b]

as the least common multiple of

a

and

b

and the notation

(a,b)

as the greatest common divisor of

a

and

b

. Find all

n \in \mathbb{N}

that satisfies

4 \sum_{k=1}^{n} [n,k] = 1 + \sum_{k=1}^{n} (n,k) + 2n^2 \sum_{k=1}^{n} \frac{1}{(n,k)}

N7