Results 51 to 60 of about 41,624 (236)
Canadian Mathematical Bulletin, 1991 AbstractLet l(N, r) be the minimum number of terms needed to express r as a sum of distinct divisors of N. Let l(N) = max{l(N, r) : 1 ≤ r ≤ N}. Then for Vose's sequence improving the result of M. Vose.
Hisashi Yokota
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 We obtain an arithmetic proof and a refinement of the inequality ϕ (nk) + σk(n) < 2nk, where n ≧ 2 and k ≧ 2. An application to another inequality is also provided.
Sándor József
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A note on solitary numbers [PDF]
Notes on Number Theory and Discrete MathematicsDoes 14 have a friend? Until now, this has been an open question. In this note, we prove that a potential friend F of 14 is an odd, non-square positive integer.
Sagar Mandal
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On normalized Laplacian spectrum of zero divisor graphs of commutative ring ℤn
Electronic Journal of Graph Theory and Applications, 2021 For a finite commutative ring ℤn with identity 1 ≠ 0, the zero divisor graph Γ(ℤn) is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices x and y are adjacent if and only if xy=0.
S. Pirzada +3 more
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Finite connected components of the aliquot graph [PDF]
, 2017 Conditional on a strong form of the Goldbach conjecture, we determine all finite connected components of the aliquot graph containing a number less than $10^9$, as well as those containing an amicable pair below $10^{14}$ or one of the known perfect or ...
Booker, Andrew R.
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On Karatsuba's Problem Concerning the Divisor Function $\tau(n)$
, 2010 We study an asymptotic behavior of the sum $\sum\limits_{n\le x}\frac{\D \tau(n)}{\D \tau(n+a)}$.
A.A. Karatsuba +5 more
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An Integer as a Sum of Consecutive Integers [PDF]
, 1999 This is a simple study of expressions of positive integers as sums of consecutive integers. In the first part proof is given for the fact that N can ben expressed in exactly d(L)-1 ways as a sum of consecutive integers, L is the largest odd factor of N ...
Ibstedt, Henry
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DISTRIBUTION OF VALUES OF THE SUM OF UNITARY DIVISORS IN RESIDUE CLASSES
Проблемы анализа, 2016 In this paper we prove the tauberian type theorem containing the asymptotic series for the Dirichlet series. We use this result to study distribution of sum of unitary divisors in residue classes coprime with a module.
B. M. Shirokov, L. A. Gromakovskaya
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Arithmatical consequences of two identities of B. Gordon
International Journal of Mathematics and Mathematical Sciences, 1979 From two partition identities of Basil Gordon the author derives two recursive formulas for the sum-of-divisors function. A third application yields an alternate proof of Rmanujan's theorem on the divisibility of certain values of the partition function ...
John A. Ewell
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Sums of distinct divisors and sums of distinct units [PDF]
Proceedings of the American Mathematical Society, 1964 where the d are distinct positive divisors of M. Clearly a (M1) ?< o(M). In a recent paper [1], B. M. Stewart presented a structure theorem for the set S of integers M, for which ac(M) =oa(M). In this paper we will drop the restriction that the divisors need be positive.
openaire +2 more sources