Discovery of a most extraordinary law of numbers relating to the sum of their divisors
This paper was apparently published three times: Fuss didn't know it had been published in Bibliothéque impartiale when he put it in the Commentationes artihmeticae collectae in 1849 and again in the Opera postuma in 1862.
Euler again uses S(n) to denote the sum of the divisors of n, and presents the various properties of the function. It's possible that much of the material here is also in E152, though this paper also has some properties of partitions (starting in section 9).
Original Source Citation
Bibliotheque impartiale, Volume 3, pp. 10-31.
Opera Omnia Citation
Series 1, Volume 2, pp.241-253.