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Search: id:A002093
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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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+0
20
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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; listen)
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OFFSET
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1,2
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COMMENT
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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
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 842.
L. Alaoglu and P. Erdos, 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
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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
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MATHEMATICA
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a={}; k=0; Do[p=Plus@ @Divisors[n]; If[p>k, AppendTo[a, n]; k=p], {n, 1, 25^2}]; a (Vladimir Orlovsky, Jul 25 2008)
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PROGRAM
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(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
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Cf. A034091, A000203, A004394.
The record values are in A034885.
Sequence in context: A005705 A139542 A093717 this_sequence A067069 A100497 A088881
Adjacent sequences: A002090 A002091 A002092 this_sequence A002094 A002095 A002096
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Better description Apr 15 1997. More terms from Jud McCranie, Jul 04 2000.
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