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pro vyhledávání: '"Practical number"'
Akademický článek
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Autor:
Carlo Sanna
Publikováno v:
Quaestiones Mathematicae; Vol. 44 No. 9 (2021); 1141-1144
A practical number is a positive integer $n$ such that all positive integers less than $n$ can be written as a sum of distinct divisors of $n$. Leonetti and Sanna proved that, as $x \to +\infty$, the central binomial coefficient $\binom{2n}{n}$ is a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::46fb4a6737ea1098863d60a071f986b8
https://doi.org/10.2989/16073606.2020.1775156
https://doi.org/10.2989/16073606.2020.1775156
Autor:
X.-H. Wu
Publikováno v:
Acta Mathematica Hungarica. 160:405-411
A positive integer n is called practical if every positive integer $$m \leq n$$ can be written as a sum of distinct divisors of n. For any integers $$a, b, k > 0$$, we show that if $$2 \nmid a$$, then there are infinitely many nonnegative integers m
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https://explore.openaire.eu/search/publication?articleId=doi_________::951a2801d2d5b11dca306d2ff724a618
https://doi.org/10.1007/s10474-019-00978-7
https://doi.org/10.1007/s10474-019-00978-7
Autor:
Carlo Sanna
Publikováno v:
Quaestiones Mathematicae; Vol 42, No 7 (2019); 977–983
A practical number is a positive integer n such that all the positive integers m ≤ n can be written as a sum of distinct divisors of n. Let (un)n≥0 be the Lucas sequence satisfying u0 = 0, u1 = 1, and un+2 = aun+1 + bun for all integers n ≥ 0,
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1ce77e1542a64b5f81f03975bcff293f
https://doi.org/10.2989/16073606.2018.1502697
https://doi.org/10.2989/16073606.2018.1502697
Akademický článek
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Autor:
Jin-Hui Fang, Yong-Gao Chen
Publikováno v:
Journal of Number Theory. 182:258-270
Text A positive integer n is called weakly prime-additive if n has at least two distinct prime divisors and there exist distinct prime divisors p 1 , … , p t of n and positive integers α 1 , … , α t such that n = p 1 α 1 + ⋯ + p t α t . It
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https://explore.openaire.eu/search/publication?articleId=doi_________::68a6f5f0c76f12633435eebdb090884c
https://doi.org/10.1016/j.jnt.2017.06.013
https://doi.org/10.1016/j.jnt.2017.06.013
Autor:
Dongho Byeon, Keunyoung Jeong
Publikováno v:
Journal of Number Theory. 179:240-255
In this paper, we show that for any given integer k ≥ 2 , there are infinitely many cube-free integers n having exactly k prime divisors such that n is a sum of two rational cubes. This is a cubic analogue of the work of Tian [Ti] , which proves th
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https://explore.openaire.eu/search/publication?articleId=doi_________::323506770534dd21aeb81ed9f9777b49
https://doi.org/10.1016/j.jnt.2017.03.011
https://doi.org/10.1016/j.jnt.2017.03.011
Autor:
Florian Luca, Carlos Alexis Gómez Ruiz
Publikováno v:
Indagationes Mathematicae
Let ( F m ) m ≥ 0 be the Fibonacci sequence given by F 0 = 0 , F 1 = 1 and F m + 2 = F m + 1 + F m , for all m ≥ 0 . In Castillo (2015), it is conjectured that 2 , 5 and 34 are the only Fibonacci numbers of the form n ! + n ( n + 1 ) 2 , for some
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fc733f60bc1469f908307bc2e82e4afc
https://doi.org/10.1016/j.indag.2017.05.002
https://doi.org/10.1016/j.indag.2017.05.002
Autor:
Andreas Weingartner, Carl Pomerance
A number $n$ is practical if every integer in $[1,n]$ can be expressed as a subset sum of the positive divisors of $n$. We consider the distribution of practical numbers that are also shifted primes, improving a theorem of Guo and Weingartner. In add
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a1bf2e3ce20516f3eef77c8d76923c6d
Autor:
Paolo Leonetti, Carlo Sanna
A "practical number" is a positive integer $n$ such that every positive integer less than $n$ can be written as a sum of distinct divisors of $n$. We prove that most of the binomial coefficients are practical numbers. Precisely, letting $f(n)$ denote
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5c56ae633a15296c7be4e1da51ea375b
http://arxiv.org/abs/1905.12023
http://arxiv.org/abs/1905.12023