Note on the function \(\zeta_1(n)\) which expresses the sum of divisors of \(n\). (Q1564766)
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scientific article; zbMATH DE number 2721453
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Note on the function \(\zeta_1(n)\) which expresses the sum of divisors of \(n\). |
scientific article; zbMATH DE number 2721453 |
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Note on the function \(\zeta_1(n)\) which expresses the sum of divisors of \(n\). (English)
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1869
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Ist \(n=aq\) und \(q\) wieder durch \(a\) theilbar, so hat man \[ \zeta_\mu(aq)+a^\mu \zeta_\mu \left(\frac{q}{a}\right)=(a^\mu+1)\zeta_\mu(q), \] wo \(\zeta_\mu\) die Summe der \(\mu^{\text{ten}}\) Potenzen der Divisoren von \(m\) bedeutet. Diese Formel ist von Bedeutung, da \(\zeta_\mu\) in dem Ausdruck für die Anzahl der, Darstellungen einer ganzen Zahl durch eine Summe von 4 Quadraten erscheint.
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Sum of divisors
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Sum of four squares
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