Recurrences for the Sum of Divisors
نویسندگان
چکیده
منابع مشابه
Iterating the Sum-of-Divisors Function
1991 Mathematics Subject Classi cation: 11A25, 11Y70 Let 0(n) = n and m(n) = ( m 1(n)), where m 1 and is the sum-of-divisors function. We say that n is (m; k)perfect if m(n) = kn. We have tabulated all (2; k)-perfect numbers up to 109 and all (3; k)and (4; k)-perfect numbers up to 2 108. These tables have suggested several conjectures, some of which we prove here. We ask in particular: For any ...
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15 صفحه اولQuadratic Recurrences with a Positive Density of Prime Divisors
For f(x) ∈ Z[x] and a ∈ Z, we let f(x) be the nth iterate of f(x), P (f, a) = {p prime : p|f(a) for some n}, and D(P (f, a)) denote the natural density of P (f, a) within the set of primes. A conjecture of Jones [5] indicates that D(P (f, a)) = 0 for most quadratic f . In this paper, we find an exceptional family of (f ,a) such that D(P (f, a)) > 0 by considering ft(x) = (x + t) − 2 − t and at ...
متن کاملThe range of the sum-of-proper-divisors function
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1977
ISSN: 0002-9939
DOI: 10.2307/2041430