Results 81 to 90 of about 31,208 (175)

On equal consecutive values of multiplicative functions

Discrete Analysis
On equal consecutive values of multiplicative functions, Discrete Analysis 2024:12, 20 pp. It is widely expected that the prime factorizations of a pair of large consecutive natural numbers $n, n+1$ (or of a pair with fixed spacing, such as $n,n+2 ...
Alexander P. Mangerel
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The multinomial convolution sums of certain divisor functions

Journal of Mathematical Analysis and Applications, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cho, Bumkyu, Kim, Daeyeoul, Park, Ho
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EVALUATING CONVOLUTION SUMS OF THE DIVISOR FUNCTION BY QUASIMODULAR FORMS [PDF]

International Journal of Number Theory, 2007
We provide a systematic method to compute arithmetic sums including some previously computed by Alaca, Besge, Cheng, Glaisher, Huard, Lahiri, Lemire, Melfi, Ou, Ramanujan, Spearman and Williams. Our method is based on quasimodular forms. This extension of modular forms has been constructed by Kaneko and Zagier.
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Exact Formulas for the Generalized Sum-of-Divisors Functions

, 2017
We prove new exact formulas for the generalized sum-of-divisors functions, $σ_α(x) := \sum_{d|x} d^α$. The formulas for $σ_α(x)$ when $α\in \mathbb{C}$ is fixed and $x \geq 1$ involves a finite sum over all of the prime factors $n \leq x$ and terms involving the $r$-order harmonic number sequences and the Ramanujan sums $c_d(x)$.
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Summing μ ( n ) : a faster elementary algorithm. [PDF]

Res Number Theory, 2023
Helfgott HA, Thompson L.
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CONVOLUTION SUMS OF ODD AND EVEN DIVISOR FUNCTIONS

Honam Mathematical Journal, 2013
Let denote the sum of the s-th power of the positive divisors of N and with , > 0 and . In a celebrated paper [33], Ramanuja proved using elementary arguments. The coefficients' relation in this identity () motivated us to write this article. In this article, we found the convolution sums for odd and even divisor functions with , , and . If N is an odd
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A note on generating identities for multiplicative arithmetic functions [PDF]

Contributions to Mathematics
Karol Gryszka
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Sums of the divisor and unitary divisor functions.

Journal für die reine und angewandte Mathematik (Crelles Journal), 1978
Suryanarayana, D., Subbarao, M.V.
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Matroid psi classes. [PDF]

Sel Math New Ser, 2022
Dastidar J, Ross D.
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Triple convolution sums of the generalised divisor functions

arXiv admin note: text overlap with arXiv:2508 ...
Misra, Bikram, Saha, Biswajyoti
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