This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A128702 #19 Jan 12 2016 04:38:03
%S A128702 16,96,168,47880,85680,95760,388080,458640,526680,609840,637560,
%T A128702 776160,887040,917280,942480,1219680,1244880,1607760,1774080,2439360,
%U A128702 3880800,5266800,5569200,6098400,7761600,9424800,12196800,17907120,20900880
%N A128702 Highly abundant numbers (A002093) that are not Harshad numbers (A005349).
%C A128702 All superabundant numbers (A004394), colossally abundant numbers (A004490), highly composite numbers (A002182) and superior highly composite numbers (A002201) are Harshad numbers. However, this is not true of the highly abundant numbers (A002093) and there are 32 exceptions in the 394 highly abundant numbers less than 50 million.
%C A128702 The previous comment is erroneous. The first superabundant number that is not a Harshad number is A004394(105) = 149602080797769600. The first highly composite number that is not a Harshad number is A002182(61) = 245044800. For all exceptions I found, the sum of digits is a power of 3. Although the first 60000 terms of the colossally abundant numbers and the superior highly composite numbers are Harshad numbers, I am not aware of a proof that all terms are Harshad numbers. There may be large counterexamples. [_T. D. Noe_, Oct 27 2009]
%H A128702 Giovanni Resta, <a href="/A128702/b128702.txt">Table of n, a(n) for n = 1..400</a>
%H A128702 L. Alaoglu and P. Erdős, <a href="http://www.renyi.hu/~p_erdos/1944-03.pdf">On highly composite and similar numbers</a>, Trans. Amer. Math. Soc., 56 (1944), 448-469.
%H A128702 Wikipedia, <a href="http://en.wikipedia.org/wiki/Highly_abundant_number">Highly Abundant Numbers</a>.
%H A128702 Wikipedia, <a href="http://en.wikipedia.org/wiki/Harshad_number">Harshad Number</a>.
%F A128702 The highly abundant numbers (A002093) are those values of n for which sigma(n)>sigma(m) for all m<n, where sigma(n)= A000203(n). Harshad numbers (A005349) are divisible by the sum of their digits.
%e A128702 The third highly abundant number that is not a Harshad number is 168. So a(3)=168.
%t A128702 hadata1=FoldList[Max,1,Table[DivisorSigma[1,n],{n,2,10^6}]]; data1=Flatten[Position[hadata1,#,1,1]&/@Union[hadata1]];HarshadQ[k_]:=If[IntegerQ[ k/(Plus @@ IntegerDigits[ k ])],True,False];Select[data1,!HarshadQ[ # ] &]
%Y A128702 Cf. A002093, A005349, A000203, A004394, A004490, A002182, A002201, A128699, A128700, A128701.
%K A128702 nonn,base
%O A128702 1,1
%A A128702 _Ant King_, Mar 28 2007
%E A128702 a(16)-a(29) from _Donovan Johnson_, May 09 2009