Divisor function: Difference between revisions

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Other properties and identities: p < q ⇒ p ≠ q, verbal clarification is superfluous; 2^k is not an "example" but a defining predicate with a free variable {{mvar|k}}; clarify the pairwise use of *generalized* pentagonal numbers in Euler's recurrence; fix a dead URL to Euler archive; minor copy-ed; canonicalize mark up only unmarked math in text only, the minimum for immediate readability, per WP:MATH.
Other properties and identities: Fixed typo, only sum natural i
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:<math>\begin{align}
\sigma(n) &= \sigma(n-1)+\sigma(n-2)-\sigma(n-5)-\sigma(n-7)+\sigma(n-12)+\sigma(n-15)+ \cdots \\[12mu]
&= \sum_{i\in\ZN} (-1)^{i+1}\left( \sigma \left( n-\frac{1}{2} \left( 3i^2-i \right) \right) + \sigma \left( n-\frac{1}{2} \left( 3i^2+i \right) \right) \right)
\end{align}</math>