DLMF:27.11.E4 (Q8073)

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DLMF:27.11.E4
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    n x σ 1 ( n ) = π 2 12 x 2 + O ( x ln x ) . subscript 𝑛 𝑥 divisor-sigma 1 𝑛 2 12 superscript 𝑥 2 Big-O 𝑥 𝑥 {\displaystyle{\displaystyle\sum_{n\leq x}\sigma_{1}\left(n\right)=\frac{{\pi^% {2}}}{12}x^{2}+O\left(x\ln x\right).}}
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    DLMF:27.11.E4
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    x 2 𝑥 2 {\displaystyle{\displaystyle x\geq 2}}
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    O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2acdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
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    σ α ( n ) divisor-sigma 𝛼 𝑛 {\displaystyle{\displaystyle\sigma_{\NVar{\alpha}}\left(\NVar{n}\right)}}
    C27.S2.E10.m2adec
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    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2abdec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C27.S1.XMD4.m1cdec
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