Image:Divisor-summatory.svg

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[edit] Divisor summatory function

This graph illustrates the divisor summatory function with the leading asymptotic terms subtracted. That is, it is a graph of

D (x) - x log x - x (2γ - 1)

where $D (x)$ is the divisor summatory function

$D(x)=\sum_{n\le x} d(n)$

and $d (n)$ is the divisor function. Here, $\gamma=0.577\ldots$ is the Euler-Mascheroni constant. The graph extends up to $x = 10 4$ . The green lines that do not quite bound the picture are a graph of $\pm 2x^{7/22}$ and give a general scale for the rate of growth for this function. Curiously, note that the function is not centered on the zero axis, but seems to be closer to the upper curve.

[edit] Licensing

Created by Linas Vepstas User:Linas 12 July 2006

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.

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(del) (cur) 16:57, 13 July 2006 . . Linas (Talk | contribs) . . 600×480 (35,369 bytes) (new imroved)
(del) (rev) 04:16, 13 July 2006 . . Linas (Talk | contribs) . . 600×480 (24,599 bytes) (fix typo in image legend)
(del) (rev) 04:04, 13 July 2006 . . Linas (Talk | contribs) . . 600×480 (24,599 bytes) (Divisor sumatory function. Created by Linas Vepstas User:Linas 12 July 2006)