منابع مشابه
On Perfect Totient Numbers
Let n > 2 be a positive integer and let φ denote Euler’s totient function. Define φ(n) = φ(n) and φ(n) = φ(φ(n)) for all integers k ≥ 2. Define the arithmetic function S by S(n) = φ(n) + φ(n) + · · ·+ φ(n) + 1, where φ(n) = 2. We say n is a perfect totient number if S(n) = n. We give a list of known perfect totient numbers, and we give sufficient conditions for the existence of further perfect ...
متن کاملOn Totient Abundant Numbers
In this note, we find an asymptotic formula for the counting function of the set of totient abundant numbers.
متن کاملOn Sparsely Schemmel Totient Numbers
For each positive integer r, let Sr denote the rth Schemmel totient function, a multiplicative arithmetic function defined by Sr(p) = ( 0, if p r; p↵ 1(p r), if p > r for all primes p and positive integers ↵. The function S1 is simply Euler’s totient function . Masser and Shiu have established several fascinating results concerning sparsely totient numbers, positive integers n satisfying (n) ...
متن کاملCyclic Group Actions on Polynomial Rings
We consider a cyclic group of order p acting on a module incharacteristic p and show how to reduce the calculation of the symmetric algebra to that of the exterior algebra. Consider a cyclic group of order p acting on a polynomial ring S = k[x1, . . . , xr], where k is a field of characteristic p; this is equivalent to the symmetric algebra S∗(V ) on the module V generated by x1, . . . , xr. We...
متن کاملThe Auslander-Reiten Conjecture for Group Rings
This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1987
ISSN: 0166-8641
DOI: 10.1016/0166-8641(87)90011-3