Borho, W. "Über die Fixpunkte der -fach iterierten Teilerersummenfunktion." Mitt. Math. Gesellsch. Hamburg9, 34-48, 1969.Cohen, H. "On Amicable and Sociable Numbers." Math. Comput.24, 423-429, 1970.Cohen, G. L. and te Riele, H. J. J. "Iterating the Sum-of-Divisors Function." Amsterdam, Netherlands: Centrum voor Wiskunde en Informatica Report NM-R9525 1995.Creyaufmüller, W. "Aliquot Sequences." http://www.aliquot.de/aliquote.htm.Devitt, J. S.; Guy, R. K.; and Selfridge, J. L. Third Report on Aliquot Sequences, Congr. Numer. XVIII, Proc. 6th Manitoba Conf. Numerical Math, pp. 177-204, 1976.Erdős, P.; Granville, A.; Pomerance, C.; and Spiro, C. "On the Normal Behavior of Iterates of Some Arithmetical Functions." Analytic Number Theory, Proc. Conf. in Honor of P. T. Bateman, Allerton Park, 1989. Boston: Birkhäuser, pp. 165-204, 1990.Flammenkamp, A. "New Sociable Numbers." Math. Comput.56, 871-873, 1991.Gardner, M. "Perfect, Amicable, Sociable." Ch. 12 in Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from Scientific American. New York: Vintage, pp. 160-171, 1978.Guy, R. K. "Aliquot Cycles or Sociable Numbers." §B7 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 62-63, 1994.Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 145-146, 1979.Moews, D. "A List of Aliquot Cycles of Length Greater than 2." Rev. Jul. 20, 2005. http://djm.cc/sociable.txt.Moews, D. "Sociable Numbers." http://djm.cc/amicable.html#sociable.Moews, D. and Moews, P. C. "A Search for Aliquot Cycles Below ." Math. Comput.57, 849-855, 1991.Moews, D. and Moews, P. C. "A Search for Aliquot Cycles and Amicable Pairs." Math. Comput.61, 935-938, 1993.Pedersen, J. A. M. "Tables of Aliquot Cycles." http://amicable.homepage.dk/tables.htm.Poulet, P. Question 4865. L'interméd. des Math.25, 100-101, 1918.Root, S. Item 61 in Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, p. 23, Feb. 1972. http://www.inwap.com/pdp10/hbaker/hakmem/number.html#item61.Sloane, N. J. A. Sequences A003416, A052470, A090615, and A119478 in "The On-Line Encyclopedia of Integer Sequences."te Riele, H. J. J. "Perfect Numbers and Aliquot Sequences." In Computational Methods in Number Theory, Part I. (Ed. H. W. Lenstra Jr. and R. Tijdeman). Amsterdam, Netherlands: Mathematisch Centrum, pp. 141-157, 1982.
，而 
是通常的除數函式。
，則該數字稱為 t 階親和數 
。 例如，1264460 是一個 4 階親和數，因為它的真因子序列為 1264460, 1547860, 1727636, 1305184, 1264460, ....
-階親和數
，則
-多完全數的定義。 如果序列 
在 
項後變為迴圈，則它被稱為 
-階親和數 
。
和 
是不同的梅森素數，則
和 
是 2 階 1/2 親和數。
的廣義 
-真因子序列的最小成員。
-fach iterierten Teilerersummenfunktion." Mitt. Math. Gesellsch. Hamburg 9, 34-48, 1969.Cohen, H. "On Amicable and Sociable Numbers." Math. Comput. 24, 423-429, 1970.Cohen, G. L. and te Riele, H. J. J. "Iterating the Sum-of-Divisors Function." Amsterdam, Netherlands: Centrum voor Wiskunde en Informatica Report NM-R9525 1995.Creyaufmüller, W. "Aliquot Sequences." 
." Math. Comput. 57, 849-855, 1991.Moews, D. and Moews, P. C. "A Search for Aliquot Cycles and Amicable Pairs." Math. Comput. 61, 935-938, 1993.Pedersen, J. A. M. "Tables of Aliquot Cycles."