单词 | Multiperfect Number | |||||||||||||||
释义 | Multiperfect NumberA number ![]() for some Integer ![]() ![]() ![]() ![]() ![]() ![]() ![]() The following table gives the first few ![]() ![]()
In 1900-1901, Lehmer proved that As of 1911, 251 pluperfect numbers were known (Carmichael and Mason 1911). As of 1929, 334 pluperfect numbers were known,many of them found by Poulet. Franqui and García (1953) found 63 additional ones (five An outdated database is maintained by R. Schroeppel, who lists 2,094 multiperfects, and an up-to-date list byJ. L. Moxham (1998). It is believed that all multiperfect numbers of index 3, 4, 5, 6, and 7 are known. The number ofknown If
Brown, A. L. ``Multiperfect Numbers.'' Scripta Math. 20, 103-106, 1954. Dickson, L. E. History of the Theory of Numbers, Vol. 1: Divisibility and Primality. New York: Chelsea, pp. 33-38, 1952. Flammenkamp, A. ``Multiply Perfect Numbers.'' http://www.uni-bielefeld.de/~achim/mpn.html. Franqui, B. and García, M. ``Some New Multiply Perfect Numbers.'' Amer. Math. Monthly 60, 459-462, 1953. Franqui, B. and García, M. ``57 New Multiply Perfect Numbers.'' Scripta Math. 20, 169-171, 1954. Guy, R. K. ``Almost Perfect, Quasi-Perfect, Pseudoperfect, Harmonic, Weird, Multiperfect and Hyperperfect Numbers.'' §B2 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 45-53, 1994. Helenius, F. W. ``Multiperfect Numbers (MPFNs).'' http://pweb.netcom.com/~fredh/mpfn/. Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 149-151, 1979. Moxham, J. L. ``13 New MPFN's.'' math-fun@cs.arizona.edu posting, Aug 13, 1998. Poulet, P. La Chasse aux nombres, Vol. 1. Brussels, pp. 9-27, 1929. Schroeppel, R. ``Multiperfect Numbers-Multiply Perfect Numbers-Pluperfect Numbers-MPFNs.'' Rev. Dec. 13, 1995. ftp://ftp.cs.arizona.edu/xkernel/rcs/mpfn.html. Schroeppel, R. (moderator). mpfn mailing list. e-mail rcs@cs.arizona.edu to subscribe. Sloane, N. J. A. Sequences A027687,A046060,A046061,A000396/M4186, andA005820/M5376in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html. |
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