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

Author

T. D. Noe, May 09 2006

Keywords

• nonn

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

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Richard Laatsch, Measuring the abundancy of integers, Mathematics Magazine 59 (2) (1986) 84-92.
• Walter Nissen, Abundancy : Some Resources

Crossrefs

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

Cf. also A171929, A228059, A386423.

Programs

Mathematica

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

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

Extensions

Definition clarified by Jonathan Sondow, Dec 08 2011