IJPAM: Volume 98, No. 2 (2015)

ON THE DIVISORS OF ORDER $r$

Andrew V. Lelechenko$^1$, Yakov A. Vorobyov$^2$
$^{1,2}$Computational Algebra and Discrete Mathematics
Odessa National University
Dvoryanskaya st. 2, Odessa, 65026, UKRAINE


Abstract. N. Minculete has introduced the divisor-of-order-$r$ function $\tau^{(r)}$ and the sum-of-divisors-of-order-$r$ function $\sigma^{(r)}$. We investigate the asymptotic behaviour of $\sum_{n\leq x} \tau^{(r)}(n)$ and $ \sum_{n\leq x}\sigma^{(r)}(n)$ and improve known estimates.

Received: June 2, 2014

AMS Subject Classification: 11A25, 11N37

Key Words and Phrases: divisor of order $r$, exponential semiproper divisor, average order

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DOI: 10.12732/ijpam.v98i2.2 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 98
Issue: 2
Pages: 181 - 192


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