Geodesic
On A theorem of Niven
Canadian mathematical bulletin, Tome 17 (1974) no. 1, pp. 109-110

Voir la notice de l'article provenant de la source Cambridge University Press

In [3], Niven proved that for any positive integer k, the density of the set of positive integers n for which (n, (φ(n))≤k is zero (where φ is the Euler to tient function). In this paper, we prove a related result—namely if k and j are any positive integers, then the density of the set of positive integers n for which (n,σj(n))≤k is zero (where σj(n) is the sum of the jth powers of the positive divisors of n). We will borrow from Niven’s technique, but we must make some crucial modifications. 
On A theorem of Niven. Canadian mathematical bulletin, Tome 17 (1974) no. 1, pp. 109-110. doi: 10.4153/CMB-1974-019-5
@misc{10_4153_CMB_1974_019_5,
     title = {On {A} theorem of {Niven}},
     journal = {Canadian mathematical bulletin},
     pages = {109--110},
     year = {1974},
     volume = {17},
     number = {1},
     doi = {10.4153/CMB-1974-019-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-019-5/}
}
TY  - JOUR
TI  - On A theorem of Niven
JO  - Canadian mathematical bulletin
PY  - 1974
SP  - 109
EP  - 110
VL  - 17
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-019-5/
DO  - 10.4153/CMB-1974-019-5
ID  - 10_4153_CMB_1974_019_5
ER  - 
%0 Journal Article
%T On A theorem of Niven
%J Canadian mathematical bulletin
%D 1974
%P 109-110
%V 17
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-019-5/
%R 10.4153/CMB-1974-019-5
%F 10_4153_CMB_1974_019_5

[1] 1. Hardy, G. H. and Wright, E. M. An Introduction to the theory of numbers. Oxford University Press, Oxford, Fourth Edition (1960). Google Scholar

[2] 2. Veque, W. J. Le, Topics in number theory, Vol. I, Addison-Wesley Publishing Co. (1958). Google Scholar

[3] 3. Niven, L., The asymptotic density of sequences, Bull. A.M.S., 57 (1951), pp. 420-434. Google Scholar

Cité par Sources :