A theorem concerning the numerical function \(\rho_2(n)\). (Q1564767)
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scientific article; zbMATH DE number 2721454
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A theorem concerning the numerical function \(\rho_2(n)\). |
scientific article; zbMATH DE number 2721454 |
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A theorem concerning the numerical function \(\rho_2(n)\). (English)
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1869
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Zerlegt man die ungrade Zahl \(n\) in irgend zwei Factoren \(d.\delta\), so bedeutet \(\rho_2(n)\) die Summe \(\sum(-1)^{\frac{\delta- 1}{2}}.d^2\). Bedeutet \(m\) irgend eine Zahl von der Form \(8k+7\), mit Ausnahme der Quadrate \(i^2\) von ungraden Zahlen, so ist: \[ \sum_{i^2<m}(m-7i^2).\rho_2\left(\frac{m-i^2}{2}\right)=0. \]
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arithmetic function involving squares of divisors
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