A119239 Oddly superabundant numbers: odd n with sigma(n)/n > sigma(k)/k for all odd k < n.

1, 3, 9, 15, 45, 105, 315, 945, 1575, 2835, 3465, 10395, 17325, 31185, 45045, 135135, 225225, 405405, 675675, 2027025, 2297295, 3828825, 6891885, 11486475, 34459425, 43648605, 72747675, 130945815, 218243025, 654729075, 1003917915, 1527701175

Offset

1,2

Comments

Every oddly colossally abundant number (A110464) is in this sequence.

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

Links

Hiroyuki Ogawa, Table of n, a(n) for n = 1..4878 (first 1000 terms from T. D. Noe)

Richard Laatsch, Measuring the abundancy of integers, Mathematics Magazine 59 (2) (1986) 84-92.

Yugo Nagamichi, Table of the first 20,685 oddly superabundant numbers

Walter Nissen, Abundancy : Some Resources.

Student Team in Semboku High School (Y.Nagamichi, Y.Yatera, H.Nakamoto, S.Haruki, K.Yamashita, K.Fujiwara, R.Sogo, Y.Uenishi), Table of the first 4500 oddly superabundant numbers (in Japanese).

Mathematica

rec=0; lst={}; Do[abun=DivisorSigma[1, n]/n; If[abun>rec, rec=abun; AppendTo[lst, n]], {n, 1, 10^6, 2}]; lst

Prog

(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

Crossrefs

Cf. A004394 (superabundant numbers), A005231 (odd abundant numbers), A053624 (highly composite odd numbers), A119240.

Cf. also A171929, A228059, A386423.

Sequence in context: A355771 A053624 A348198 * A140864 A171929 A188597

Adjacent sequences: A119236 A119237 A119238 * A119240 A119241 A119242

Keyword

nonn,changed

Author

T. D. Noe, May 09 2006

Extensions

Definition clarified by Jonathan Sondow, Dec 08 2011

Status

approved