%I A002093 M0553 N0200
%S A002093 1,2,3,4,6,8,10,12,16,18,20,24,30,36,42,48,60,72,84,90,96,108,120,144,
%T A002093 168,180,210,216,240,288,300,336,360,420,480,504,540,600,630,660,720,
%U A002093 840,960,1008,1080,1200,1260,1440,1560,1620,1680,1800,1920,1980,2100
%N A002093 Highly abundant numbers: sigma(n) > sigma(m) for all m < n.
%C A002093 Where record values of sigma(n) occur.
%C A002093 RECORDS transform of A000203.
%C A002093 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
%D A002093 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.
%D A002093 L. Alaoglu and P. Erdos, On highly composite and similar numbers, Trans. 
               Amer. Math. Soc., 56 (1944), 448-469.
%D A002093 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002093 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002093 T. D. Noe, <a href="b002093.txt">Table of n, a(n) for n=1..10000</a>
%H A002093 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A002093 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%t A002093 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)
%o A002093 (PARI) for(n=1,1000,if(sum(i=1,n-1,sign(sigma(n)-sigma(i))) == n-1,print1(n,
               ",")))
%Y A002093 Cf. A034091, A000203, A004394.
%Y A002093 The record values are in A034885.
%Y A002093 Sequence in context: A005705 A139542 A093717 this_sequence A067069 A100497 
               A088881
%Y A002093 Adjacent sequences: A002090 A002091 A002092 this_sequence A002094 A002095 
               A002096
%K A002093 nonn,nice
%O A002093 1,2
%A A002093 N. J. A. Sloane (njas(AT)research.att.com).
%E A002093 Better description Apr 15 1997. More terms from Jud McCranie, Jul 04 
               2000.