A119239 - OEIS

%I #53 Jul 21 2026 19:16:04

%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.

%C a(8) = 945 is the first term with abundancy > 2, a(41) = 1018976683725 is the first term with abundancy > 3, and a(141) = 1853070540093840001956842537745897243375 is the first term with abundancy > 4. See A119240. - _Antti Karttunen_, Jul 21 2025

%H Hiroyuki Ogawa, <a href="/A119239/b119239.txt">Table of n, a(n) for n = 1..4878</a> (first 1000 terms from T. D. Noe)

%H Richard Laatsch, <a href="https://www.jstor.org/stable/2690424">Measuring the abundancy of integers</a>, Mathematics Magazine 59 (2) (1986) 84-92.

%H Yugo Nagamichi, <a href="https://semboku-h.ed.jp/ssh/wp-content/uploads/2026/06/eafd6a6c2c420ad468bf03dbf60da60b.pdf">Table of the first 20,685 oddly superabundant numbers</a>

%H Walter Nissen, <a href="http://upforthecount.com/math/abundance.html">Abundancy : Some Resources</a>.

%H Student Team in Semboku High School (Y.Nagamichi, Y.Yatera, H.Nakamoto, S.Haruki, K.Yamashita, K.Fujiwara, R.Sogo, Y.Uenishi), <a href="https://semboku-h.ed.jp/ssh/wp-content/uploads/2026/04/b77d1045ce6beefaaf17b881cc275caf.pdf">Table of the first 4500 oddly superabundant numbers</a> (in Japanese).

%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), A119240.

%Y Cf. also A171929, A228059, A386423.

%K nonn,changed

%O 1,2

%A _T. D. Noe_, May 09 2006

%E Definition clarified by _Jonathan Sondow_, Dec 08 2011