Geodesic
The Divisibility of Divisor Functions
Glasgow mathematical journal, Tome 5 (1961) no. 1, pp. 35-40

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

For any positive integers n and v letwhere d runs through all the positive divisors of n. For each positive integer k and real x > 1, denote by N(v, k; x) the number of positive integers n ≦ x for which σv(n) is not divisible by k. Then Watson [6] has shown that, when v is odd,as x → ∞; it is assumed here and throughout that v and k are fixed and independent of x. It follows, in particular, that σ (n) is almost always divisible by k. A brief account of the ideas used by Watson will be found in § 10.6 of Hardy's book on Ramanujan [2]. 
Rankin, R. A. The Divisibility of Divisor Functions. Glasgow mathematical journal, Tome 5 (1961) no. 1, pp. 35-40. doi: 10.1017/S2040618500034274
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[1] 1.Chowla, S., On a theorem of Walfisz, J. London Math. Soc. 22 (1947), 136–140. Google Scholar | DOI

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[6] 6.Watson, G. N., Uber Ramanujansche Kongruenzeigenschaften der Zerfāllungsanzahlen (I), Math. Z. 39 (1935), 712–731. Google Scholar | DOI

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