Further Results on a Curious Arithmetic Function by Long Chen, Kaimin Cheng, Tingting Wang

“…In this paper, we introduce an arithmetic function fp:N∗⟶Q+ defined by fpn≔n/pvpn1−vpn for any positive integer n. …”
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Arithmetic functions associated with infinitary divisors of an integer by Graeme L. Cohen, Peter Hagis

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Summatory Multiplicative Arithmetic Functions: Scaling and Renormalization by Leonid G. Fel

“…We consider a wide class of summatory functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mfenced separators="" open="{" close="}"><mi>f</mi><mo>;</mo><mi>N</mi><mo>,</mo><msup><mi>p</mi><mi>m</mi></msup></mfenced><mo>=</mo><msub><mo>∑</mo><mrow><mi>k</mi><mo>≤</mo><mi>N</mi></mrow></msub><mi>f</mi><mfenced separators="" open="(" close=")"><msup><mi>p</mi><mi>m</mi></msup><mi>k</mi></mfenced></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>∈</mo><msub><mi mathvariant="double-struck">Z</mi><mo>+</mo></msub><mo>∪</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow></mrow></semantics></math></inline-formula> associated with the multiplicative arithmetic functions <i>f</i> of a scaled variable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>∈</mo><msub><mi mathvariant="double-struck">Z</mi><mo>+</mo></msub></mrow></semantics></math></inline-formula>, where <i>p</i> is a prime number. …”
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An identity for a class of arithmetical functions of several variables by Pentti Haukkanen

Subjects: “…arithmetical functions of several variables…”
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The local limit theorem of Delange in the Knopfmacher's semigroup by Rimantas Skrabutėnas

Subjects: “…arithmetic function…”
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On a function related to Ramanujan's Tau function by John A. Ewell

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Asymptotical expansions in the Kubilius theorem of large deviations by Rimantas Skrabutėnas

Subjects: “…arithmetic function…”
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A new class of infinite products, and Euler's totient by Geoffrey B. Campbell

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The effective use of remainder term estimation in the limit theorems by Rimantas Skrabutėnas

“… We investigate the asymptotic behavior of mean value of multiplicative arithmetic function from the class M1(G). In the present paper the asymptotic formula under special condition on prime elements of Knopfmacher’s semigroup G is obtained. …”
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A New Family of Degenerate Poly-Genocchi Polynomials with Its Certain Properties by Waseem A. Khan, Rifaqat Ali, Khaled Ahmad Hassan Alzobydi, Naeem Ahmed

“…Then, we also consider the degenerate unipoly-Genocchi polynomials attached to an arithmetic function, by using the degenerate polylogarithm function, and investigate some identities of those polynomials. …”
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Association of objective and subjective socioeconomic markers with cognitive impairment among older adults: cross-sectional evidence from a developing country by Shobhit Srivastava, T Muhammad, TV Sekher

“…The sample included 31 464 older adults aged 60 years and above.Primary and secondary outcome measures Outcome variable was cognitive impairment, measured through broad domains of memory, orientation, arithmetic function, and visuo-spatial and constructive skills. …”
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Asymtotical expansions in local limit theorem of large deviations by Rimantas Skrabutėnas

“… We continue investigation of the local distribution of multiplicative arithmetic functions from the class M(G). In the present paper the local limit theorem of large deviations with asymptotical expansion of the principal term is obtained. …”
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Local distributions of multiplicative functions by Rimantas Skrabutėnas

“… In the present paper the local distribution laws of values of multiplicative arithmetic functions g : G → R defined on arithmetical semigroups G and belonging to the class M(G) is considered. …”
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Notes on the divisibility of GCD and LCM Matrices by Pentti Haukkanen, Ismo Korkee

“…Let S={x1,x2,…,xn} be a set of positive integers, and let f be an arithmetical function. The matrices (S)f=[f(gcd(xi,xj))] and [S]f=[f(lcm [xi,xj])] are referred to as the greatest common divisor (GCD) and the least common multiple (LCM) matrices on S with respect to f, respectively. …”
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Fast and low‐power leading‐one detectors for energy‐efficient logarithmic computing by Mohammad Saeed Ansari, Shyama Gandhi, Bruce F. Cockburn, Jie Han

“…Abstract The logarithmic number system (LNS) can be used to simplify the computation of arithmetic functions, such as multiplication. This article proposes three leading‐one detectors (LODs) to speed up the binary logarithm calculation in the LNS. …”
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