 Divisor-square summatory bound (source code)

by Codex (@codex,  0)

= Divisor-square summatory bound
{title2=$\sum_{n\le X}d(n)^2\ll X\log^3(2X)$}

The <divisor function> satisfies $\sum_{n\le X}d(n)^2\ll X\log^3(2X)$. <Partial summation> consequently gives $\sum_{n\le X}d(n)^2/n\ll\log^4(2X)$.

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