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A007593 2-hyperperfect numbers: n=2(sigma(n)-n-1)+1.
(Formerly M5121)
6
21, 2133, 19521, 176661, 129127041 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

COMMENTS

a(6) > 10^12. - Donovan Johnson, Nov 03 2011

REFERENCES

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 21, pp 7, Ellipses, Paris 2008.

R. K. Guy, Unsolved Problems in Number Theory, B2.

Daniel Minoli, Sufficient Forms For Generalized Perfect Numbers, Ann. Fac. Sciences, Univ. Nation. Zaire, Section Mathem; Vol. 4, No. 2, Dec 1978, pp. 277-302.

Daniel Minoli, New Results For Hyperperfect Numbers, Abstracts American Math. Soc., October 1980, Issue 6, Vol. 1, pp. 561.

Daniel Minoli, Issues in non-linear hyperperfect numbers, Math. Comp., 34 (1980), 639-645.

Daniel Minoli, Structural Issues For Hyperperfect Numbers, Fibonacci Quarterly, Feb. 1981, Vol. 19, No. 1, pp. 6-14.

Daniel Minoli, Voice Over MPLS, McGraw-Hill, 2002, New York, NY, see pp. 112-134.

Daniel Minoli and Robert Bear, Hyperperfect Numbers, PME Journal, Fall 1975, pp. 153-157.

Daniel Minoli and W. Nakamine, Mersenne Numbers Rooted On 3 For Number Theoretic Transforms, 1980 IEEE International Conf. on Acoust., Speech and Signal Processing.

J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 177.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

J. S. McCranie, A study of hyperperfect numbers, J. Int. Seqs. Vol. 3 (2000) #P00.1.3

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

CROSSREFS

Sequence in context: A203327 A163928 A153848 * A119099 A033510 A123844

Adjacent sequences:  A007590 A007591 A007592 * A007594 A007595 A007596

KEYWORD

nonn,hard

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com), David W. Wilson (davidwwilson(AT)comcast.net)

EXTENSIONS

328256967373616371221, 67585198634817522935331173030319681, 443426488243037769923934299701036035201 are also in the sequence - Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Dec 16 1999

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Last modified February 12 21:29 EST 2012. Contains 205433 sequences.