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A002093
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Highly abundant numbers: sigma(n) > sigma(m) for all m < n.
(Formerly M0553 N0200)
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34
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1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 42, 48, 60, 72, 84, 90, 96, 108, 120, 144, 168, 180, 210, 216, 240, 288, 300, 336, 360, 420, 480, 504, 540, 600, 630, 660, 720, 840, 960, 1008, 1080, 1200, 1260, 1440, 1560, 1620, 1680, 1800, 1920, 1980, 2100
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Where record values of sigma(n) occur.
RECORDS transform of A000203.
Also record values of A070172: A070172(i)<a(n) for 1<=i < A085443(n), a(n)=A070172(A085443(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 30 2003
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REFERENCES
| L. Alaoglu and P. Erdös, On highly composite and similar numbers, Trans. Amer. Math. Soc., 56 (1944), 448-469.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
N. J. A. Sloane, Transforms
Wikipedia, Highly abundant number
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MATHEMATICA
| a={}; k=0; Do[s=DivisorSigma[1, n]; If[s>k, AppendTo[a, n]; k=s], {n, 3000}]; a (* Vladimir Orlovsky, Jul 25 2008 *)
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PROG
| (PARI) for(n=1, 1000, if(sum(i=1, n-1, sign(sigma(n)-sigma(i))) == n-1, print1(n, ", ")))
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CROSSREFS
| Cf. A034091, A000203, A004394.
The record values are in A034885.
Cf. A193988, A193989 (records for sigma2 and sigma3).
Sequence in context: A005705 A139542 A093717 * A179971 A067069 A100497
Adjacent sequences: A002090 A002091 A002092 * A002094 A002095 A002096
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Better description Apr 15 1997. More terms from Jud McCranie, Jul 04 2000.
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