منابع مشابه
On Φ–amicable Pairs
Let φ(n) denote Euler’s totient function, i.e., the number of positive integers < n and prime to n. We study pairs of positive integers (a0, a1) with a0 ≤ a1 such that φ(a0) = φ(a1) = (a0 + a1)/k for some integer k ≥ 1. We call these numbers φ–amicable pairs with multiplier k, analogously to Carmichael’s multiply amicable pairs for the σ–function (which sums all the divisors of n). We have comp...
متن کاملAmicable Pairs and Aliquot Sequences
This constant can, in fact, be rigorously calculated to 149 digits (and probably much higher accuracy if needed). Define () to be the th iterate of with starting value . The integer is amicable or 2-sociable if () = but () 6= . Such phrasing is based on older terminology [3]: two distinct integers , are said to form an “amicable pair” if () = and () = . The (infinite?) ...
متن کاملNew amicable four-cycles
Fifty new amicable four-cycles are discovered by the constructive method invented in 1969 by the second author. 1. Let τ(n) denote the sum of proper divisors of a natural number n, and let σ(n) = n + τ(n). We consider when the sequence n, τ(n), τ (n) := τ(τ(n)), . . . becomes periodic. If n = τ (n) with k minimal, then n1 = n, n2 = τ(n), n3 = τ (n), . . . , nk = τ (k−1)(n) is called an amicable...
متن کاملNew amicable pairs of type (2, 2) and type (3, 2)
A UBASIC computer program was developed to implement a method of te Riele for finding amicable pairs of type (2, 2). Hundreds of new pairs were found, including a new largest (2, 2) pair and several “daughter”, “granddaughter”, and “great granddaughter” pairs.
متن کاملAmicable Pairs and Aliquot Cycles for Elliptic Curves
An amicable pair for an elliptic curve E/Q is a pair of primes (p, q) of good reduction for E satisfying #Ẽp(Fp) = q and #Ẽq(Fq) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j 6= 0) have no aliqout cycles of length greate...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1994
ISSN: 0898-1221
DOI: 10.1016/0898-1221(94)00142-1