On an Integer's Infinitary Divisors

Cohen, Graeme L.

doi:10.2307/2008701

Cited by 11 publications

(34 citation statements)

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“…Examples are the financial industry, environmental management, or technical and safety requirements concerning products. 65 .…”

Section: Self-or Co-regulation?mentioning

confidence: 99%

“…Lastly, there also competition concerns if the standard setting is dominated by leading platforms, hindering new market entrants to prosper. 140 . Elevating existing technical risk management systems for infringement prevention, developed by leading platforms, to a state-ofthe art standard for the entire sector could pose high entry barriers for new, small ISPs.…”

Section: Limitations and Risksmentioning

confidence: 99%

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A risk-based approach towards infringement prevention on the internet: adopting the anti-money laundering framework to online platforms

Ullrich

2018

International Journal of Law and Information Technology

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This paper suggests a new approach towards online service provider liability which relies on duty of care. It proposes a concrete compliance framework for online platforms, borrowed from risk regulation, and modelled on anti-money laundering (AML) obligations in the financial sector. First, the prohibition on obliging platforms to monitor content in a general manner under the E-Commerce Directive will be discussed. On the face of it this may clash with a standardized requirement to filter for infringing content. Subsequently, the regulatory choice for such a duty of care standard will be explored. It is argued that the largely self-regulatory proposals currently on the table may be ill fitted to achieve traction and accountability. Finally, a three-tier compliance framework, modelled on the AML system and using a riskbased approach, is proposed. The pitfalls of such a highly automated compliance solution, which enforces complex legal norms, will also be touched on.

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“…Examples are the financial industry, environmental management, or technical and safety requirements concerning products. 65 .…”

Section: Self-or Co-regulation?mentioning

confidence: 99%

Section: Limitations and Risksmentioning

confidence: 99%

A risk-based approach towards infringement prevention on the internet: adopting the anti-money laundering framework to online platforms

Ullrich

2018

International Journal of Law and Information Technology

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“…Either a different definition of "divisor" has been adopted, as with unitary amicable numbers (see Hagis [11]) or infinitary amicable numbers (see Cohen [3]), or the conditions in ( 1 ) have been altered slightly. For the latter, see Guy [ 10] where pairs m , n with a(m) = a(n) -m + n-1 or with a(m) -a(n) = m + n+1 are discussed.…”

Section: =1mentioning

confidence: 99%

Multiamicable Numbers

Cohen¹,

Gretton²,

Hagis³

1995

Mathematics of Computation

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Abstract.Multiamicable numbers are a natural generalization of amicable numbers: two numbers form a multiamicable pair if the sum of the proper divisors of each is a multiple of the other. Many other generalizations have been considered in the past. This paper reviews those earlier generalizations and gives examples and properties of multiamicable pairs. It includes a proof that the set of all multiamicable numbers has density 0. Generalizations of amicable numbersTwo natural numbers are said to be amicable if the sum of the proper divisors of each of them equals the other. Thus, where o denotes the positive divisor sum function, m and n are amicable if (1) o(m) -m = n and o(n)-n -m. This condition can be abbreviated to a(m) = a(n) = m + n . We assume that m ^ n . (If m = n , then m is perfect.) It is usual to order pairs of amicable numbers according to the size of the smaller member. The smallest pair of amicable numbers, known to the Pythagoreans, is 220 and 284. Many of the classical mathematicians, such as Fermât, Mersenne, Descartes, Legendre, and particularly Euler, studied amicable numbers. Over fifty thousand pairs are now known, and many techniques are known for generating new pairs from old ones, although these will not always be successful. It has not been determined, however, whether there are infinitely many pairs of amicable numbers.

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“…This notation immediately induces ∞-divisor function τ ∞ (sequence A037445) and sum-of-∞-divisors function σ ∞ (sequence A049417). See Cohen [1].Recently Minculete and Tóth [15] defined and studied an exponential analogue of unitary divisors. We introduce e-∞-divisors: m | (e)∞ n if m | n and for each p | n, p a || m, p b || n, we have a | ∞ b.…”

mentioning

confidence: 99%