Perfect numbers and finite groups
Rendiconti del Seminario Matematico della Università di Padova, Tome 129 (2013), pp. 17-34. 
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     volume = {129},
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     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2013__129__17_0/}
}
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De Medts, Tom; Maróti, Attila. Perfect numbers and finite groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 129 (2013), pp. 17-34. http://www.numdam.org/item/RSMUP_2013__129__17_0/

[1] C. W. Anderson, The solution of Σ(n)=σ(n)/n=a/b , Φ(n)=ϕ(n)/n=a/b and some related considerations, unpublished manuscript (1974).

[2] T. De Medts, Recovering n from σ(n)/n , MathOverflow, http://mathoverflow.net/questions/56376.

[3] T. De Medts - M. Tărnăuceanu, Finite groups determined by an inequality of the orders of their subgroups, Bull. Belg. Math. Soc. Simon Stevin 15, no. 4 (2008), pp. 699-704. | MR

[4] B. Huppert, Endliche Gruppen I, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin, New York, 1967. | MR

[5] T. Leinster, Perfect numbers and groups, arXiv:math/0104012.

[6] T. Leinster, Is there an odd-order group whose order is the sum of the orders of the proper normal subgroups?, Math. Overflow, http://mathoverflow.net/questions/54851.

[7] W. A. Stein et. al., Sage Mathematics Software (Version 4.6.1), The Sage Development Team, 2011, http://www.sagemath.org.

[8] W. G. Stanton - J. A. Holdener, Abundancy outlaws of the form (σ(N)+t)/N , J. Integer Sequences 10 (2007), Article 09.7.6. | MR

[9] http://java.ugent.be/~tdemedts/leinster.