DLMF:27.11.E4

MaRDI QIDQ8766

• Label: DLMF:27.11.E4

Digital Library of Mathematical Functions ID 27.11.E4

${\displaystyle{\displaystyle\sum_{n\leq x}\sigma_{1}\left(n\right)=\frac{{\pi^{2}}}{12}x^{2}+O\left(x\ln x\right).}}$

Constraint(s)

${\displaystyle{\displaystyle x\geq 2}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\sigma_{\NVar{\alpha}}\left(\NVar{n}\right)}}$: sum of powers of divisors of $$n$$
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle n}}$: positive integer
• ${\displaystyle{\displaystyle x}}$: real number
 

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