Amicable Numbers and Their Distribution
نویسندگان
چکیده
منابع مشابه
On amicable numbers
Let A (x) denote the set of integers n≤ x that belong to an amicable pair. We show that #A (x)≤ x/e √ logx for all sufficiently large x.
متن کاملQuasi-Amicable Numbers are Rare
Define a quasi-amicable pair as a pair of distinct natural numbers each of which is the sum of the nontrivial divisors of the other, e.g., {48, 75}. Here nontrivial excludes both 1 and the number itself. Quasi-amicable pairs have been studied (primarily empirically) by Garcia, Beck and Najar, Lal and Forbes, and Hagis and Lord. We prove that the set of n belonging to a quasi-amicable pair has a...
متن کاملBreeding amicable numbers in abundance. II
In a first article of this title, new procedures were described to compute many amicable numbers by “breeding” them in several generations. An extensive computer search was later performed (in 1988), and demonstrated the remarkable effectiveness of this breeding method: the number of known amicable pairs was easily quadrupled by this search. As we learnt recently (1999) from the internet, Peder...
متن کاملOn Amicable Numbers With Different Parity
In this paper we provide a straightforward proof that if a pair of amicable numbers with different parity exists (one number odd and the other one even), then the odd amicable number must be a perfect square, while the even amicable number has to be equal to the product of a power of 2 and an odd perfect square. 1 Introductory remarks An amicable pair (M,N) consists of two integers M , N for wh...
متن کاملThe Reciprocal Sum of the Amicable Numbers
In this paper, we improve on several earlier attempts to show that the reciprocal sum of the amicable numbers is small, showing this sum is < 215.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1970
ISSN: 0025-5718
DOI: 10.2307/2004490