Results 11 to 20 of about 37 (34)
On a thin set of integers involving the largest prime factor function
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 19, Page 1185-1192, 2003., 2003 For each integer n ≥ 2, let P(n) denote its largest prime factor. Let S : = {n ≥ 2 : n does not divide P(n)!} and S(x) : = #{n ≤ x : n ∈ S}. Erdős (1991) conjectured that S is a set of zero density. This was proved by Kastanas (1994) who established that S(x) = O(x/logx). Recently, Akbik (1999) proved that S(x)=O(x exp{−(14/)logx}).
Jean-Marie De Koninck, Nicolas Doyon
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 3, Page 655-658, 1999., 1999 For a positive integer n, let P(n) denotes the largest prime divisor of n and define the set: 𝒮(x) = 𝒮 = {n ≤ x : n does not divide P(n)!}. Paul Erdös has proposed that |S| = o(x) as x → ∞, where |S| is the number of n ∈ S. This was proved by Ilias Kastanas. In this paper we will show the stronger result that .
Safwan Akbik
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Sec. 3 -T 23 N-R 16 E, Rogers County, Oklahoma
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core
On the distribution of powered numbers
Open MathematicsAsymptotic formulae are established for the number of natural numbers mm with largest square-free divisor not exceeding mϑ{m}^{{\vartheta }}, for any fixed positive parameter ϑ{\vartheta }. Related counting functions are also considered.
Brüdern Jörg, Robert Olivier
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On the ratio of the sum of divisors and Euler’s totient function II [PDF]
, 2014 We find the form of all solutions to ø(n) | σ(n) with three or fewer prime factors, except when the quotient is 4 and n is ...
Qizhi Zhou +3 more
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On the ratio of the sum of divisors and Euler’s Totient Function I [PDF]
, 2013 We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factors are 3, 35 and 1045. Moreover, there exist at most a finite number of solutions to σ(n)=2φ(n) with Ω(n)≤ k, and there are at most 22k+k-k squarefree ...
Delbourgo, Daniel, Broughan, Kevin A.
core
Arithmetically Related Ideal Topologies and the Infinitude of Primes
, 2004 The late J. Knopfmacher and the author [12] have studied some ties between arithmetic properties of the multiplicative structure of commutative rings with identity and the topologies induced by some coset classes. In the present communication it is
Porubský, Stefan
core
Genetic population structure of the malaria vector Anopheles baimaii in north-east India using mitochondrial DNA. [PDF]
Malar J, 2012 Sarma DK +11 more
europepmc +1 more source
Coupling of Nondegenerate Topological Modes in Nitrogen Core-Doped Graphene Nanoribbons. [PDF]
ACS NanoJacobse PH +9 more
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Dose-Response Effect of Glucagon on Glucose, Beta-Cell Secretion and Metabolism in Healthy Individuals. [PDF]
Diabetes Obes MetabBrock SB +4 more
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