Geodesic
On a Theorem of Niven
Canadian mathematical bulletin, Tome 22 (1979) no. 1, pp. 113-115

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

In [4], Niven proved that the set A of integers for all s ≥ l and all n ≥ 1 has density zero, being the sum of the sth powers of all positive divisors of n. However his argument contains a mistake (see Remark 1). In this paper we give a proof of Niven's result and establish several related results, one of which generalizes a result of Dressier (See Theorem 3 and Remark 2). 
Rao, R. Sita Rama Chandra; Murty, G. Sri Rama Chandra. On a Theorem of Niven. Canadian mathematical bulletin, Tome 22 (1979) no. 1, pp. 113-115. doi: 10.4153/CMB-1979-018-5
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[1] 1. Dickson, L. E., History of the Theory of Numbers, Vol. I, Chelsea Publishing Company (reprinted), New York, 1952. Google Scholar

[2] 2. Dressier, R. E., On a Theorem of Niven, Canad. Math. Bull., 17 (1), (1974), pp. 109-110. Google Scholar

[3] 3. Hardy, G. H. and Wright, E. M., An Introduction to the Theory of Numbers, Oxford University Press, Oxford, Fourth edition (1960). Google Scholar

[4] 4. Niven, I., The Asymptotic density of sequences, Bull. A.M.S., 57 (1951), pp. 420-434. Google Scholar

[5] 5. Niven, I. and Zuckermann, H. S., An Introduction to the Theory of Numbers, Wiley Eastern Limited, New Delhi-Bangalore, Third edition (1972). Google Scholar

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