[See also perfect and amicable numbers.]
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25295 Aria Anavi/Paul Pollack/Carl Pomerance: On congruences of the form
\sigma(n)=a (mod n). Intl. J. Number Theory 9 (2012), 115-124.

26936 Jordan Bell: Euler and the pentagonal number theorem. Arxiv 051054 (2006), 21p.

25299 Yusuke Chishiki/Takeshi Goto/Yasuo Ohno: On the largest prime divisor
of an odd harmonic number. Math. Comp 76/259 (2007), 1577-1587.

25275 Graeme Cohen/Herman te Riele: Iterating the sum-of-divisors function.
Experim. Math. 5/2 (1996), 91-100.

27357 Marc Deleglise: Bounds for the density of abundant integers.
Exper. Math. 7/2 (1998), 137-143.

25368 Paul ErdÃ¶s: Some remarks on the iterates of the \phi and \sigma functions.
Colloq. Math. 17 (1967), 195-202.

25279 Paul ErdÃ¶s/Andrew Granville/Carl Pomerance/Claudia Spiro: On the normal
behavior of the iterates of some arithmetic functions.
In B. Berndt a.o. (ed.): Analytic number theory. BirkhÃ¤user 1990, 165-204.

26929 Leonhard Euler: An observation on the sums of divisors. Arxiv 0411587 (2009), 13p.

26930 John Ewell: Recurrences for the sum of divisors.
Proc. AMS 64/2 (1977), 214-218.

26924 Florian Luca/Carl Pomerance: On some problems of Makowski-Schinzel
and ErdÃ¶s concerning the arithmetical functions \phi and \sigma.
Coll. Math. 92/1 (2002), 111-130.

26927 A. Makowski. On some equations involving functions \phi(n) and \sigma(n).
Am. Math. Monthly 67 (1960), 668-670.

26923 Walter Mientka/Richard Vogt: Computational results relating to problems
concerning \sigma(n). Mat. Vestnik 7 (1970), 35-36.

26935 Jean Pierre Mutanguha: Euler's pentagonal number theorem. Internet 2013, 4p.

26931 Ivan Niven: Formal power series. Am. Math. Monthly 76 (1969), 871-889.

26932 Thomas Osler/Abdulkadir Hassen/Tirupathi Chandrupatla.
Surprising connections between partitions and divisors.
Coll. Math. J. 38/4 (2007), 278-287.

27428 Paul Pollack: On the greatest common divisor of a number
and its sum of divisors. Mich. Math. J. 60 (2011), 199-214.

25300 Paul Pollack/Carl Pomerance: Prime-perfect numbers. Integers 12A (2012), 19p.
n is called prime-perfect, if n and \sigma(n) share the same set of distinct prime divisors.

25421 Herman te Riele: A theoretical and computational study of generalized
aliquot sequences. Math. Centre Tracts 74 (1976), 88p.

25422 Herman te Riele: Further results on unitary aliquot sequences.
Math. Centre Tracts 78/2 (1978), 67p.

25277 Jozsef Sandor/Dragoslav Mitrinovic/Borislav Crstici: Handbook of
number theory I. Springer 2006, 640p. Eur 132.

29023 Dimitris Vartziotis/Aristos Tzavellas: On sums of prime factors. Arxiv 1607.008521 (2017), 4p.

26928 Andreas Weingartner: On the solutions of \sigma(n)=\sigma(n+k).
J. Int. Sequences 14 (2011), 7p.

25282 Qizhi Zhou: Multiply perfect numbers of low abundancy.
PhD thesis Univ. Waikato 2010, 150p.