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A033880
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Abundance of n, or (sum of divisors of n) - 2n.
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21
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-1, -1, -2, -1, -4, 0, -6, -1, -5, -2, -10, 4, -12, -4, -6, -1, -16, 3, -18, 2, -10, -8, -22, 12, -19, -10, -14, 0, -28, 12, -30, -1, -18, -14, -22, 19, -36, -16, -22, 10, -40, 12, -42, -4, -12, -20, -46, 28, -41, -7, -30, -6, -52, 12, -38, 8, -34, -26, -58, 48, -60, -28, -22
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| For no known n is a(n) = 1. If there is such an n it must be greater than 10^35 and have seven or more distinct prime factors (Hagis and Cohen 1982) [Jonathan Vos Post, May 1, 2011].
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REFERENCES
| Hagis, P.; and Cohen, G. L. "Some Results Concerning Quasiperfect Numbers." J. Austral. Math. Soc. Ser. A 33, 275-286, 1982.
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.
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LINKS
| J. G. Wurtzel, Table of n, a(n) for n=1..10000 [This replaces an earlier b-file computed by T. D. Noe]
Eric Weisstein's World of Mathematics, Abundance
Eric Weisstein's World of Mathematics, Quasiperfect Number
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FORMULA
| a(n) = A000203(n)-A005843(n). [From Omar E. Pol, Dec 14 2008]
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MAPLE
| with(numtheory); n->sigma(n) - 2*n;
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MATHEMATICA
| Array[Total[Divisors[#]]-2#&, 70] (* From Harvey P. Dale, Sep 16 2011 *)
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CROSSREFS
| Equals -A033879. Cf. A005100.
Sequence in context: A120112 A103977 A109883 * A033879 A033883 A106316
Adjacent sequences: A033877 A033878 A033879 * A033881 A033882 A033883
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KEYWORD
| sign,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Definition corrected Jul 04 2005
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