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A007592
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Hyperperfect numbers: k = m*(sigma(k) - k - 1) + 1 for some m > 1.
(Formerly M5113)
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6
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21, 301, 325, 697, 1333, 1909, 2041, 2133, 3901, 10693, 16513, 19521, 24601, 26977, 51301, 96361, 130153, 159841, 163201, 176661, 214273, 250321, 275833, 296341, 306181, 389593, 486877, 495529, 542413, 808861, 1005421, 1005649, 1055833, 1063141, 1232053
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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D. Minoli, Sufficient Forms For Generalized Perfect Numbers, Ann. Fac. Sciences, Univ. Nation. Zaire, Section Mathem; Vol. 4, No. 2, Dec 1978, pp. 277-302.
D. Minoli, New Results For Hyperperfect Numbers, Abstracts American Math. Soc., October 1980, Issue 6, Vol. 1, pp. 561.
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).
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LINKS
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MATHEMATICA
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hpnQ[n_]:=Module[{den=DivisorSigma[1, n]-n-1, c}, If[den!=0, c=(n-1)/den, c=Pi]; IntegerQ[c]&&c>1]; Select[Range[1250000], hpnQ] (* Harvey P. Dale, Aug 11 2012 *)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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