%I #13 Aug 29 2015 04:24:03
%S 1,3,9,15,45,105,315,945,1575,2835,3465,10395,17325,31185,45045,
%T 135135,225225,405405,675675,2027025,2297295,3828825,6891885,11486475,
%U 34459425,43648605,72747675,130945815,218243025,654729075,1003917915,1527701175
%N Oddly superabundant numbers: odd n with sigma(n)/n > sigma(k)/k for all odd k < n.
%C Every oddly colossally abundant number (A110464) is in this sequence.
%H T. D. Noe, <a href="/A119239/b119239.txt">Table of n, a(n) for n = 1..1000</a>
%H Richard Laatsch, <a href="http://www.jstor.org/stable/2690424">Measuring the abundancy of integers</a>, Mathematics Magazine 59 (2) (1986) 84-92.
%H Walter Nissen, <a href="http://upforthecount.com/math/abundance.html">Abundancy : Some Resources </a>
%t rec=0; lst={}; Do[abun=DivisorSigma[1,n]/n; If[abun>rec, rec=abun; AppendTo[lst,n]], {n,1,10^6,2}]; lst
%o (PARI) r=0;forstep(n=1,1e6,2,t=sigma(n)/n;if(t>r,r=t;print1(n", "))) \\ _Charles R Greathouse IV_, Nov 27 2013
%Y Cf. A004394 (superabundant numbers), A005231 (odd abundant numbers), A053624 (highly composite odd numbers).
%K nonn
%O 1,2
%A _T. D. Noe_, May 09 2006
%E Definition clarified by _Jonathan Sondow_, Dec 08 2011