A307122 3-deficient numbers with increasing abundancy: Numbers k such that sigma(m)/m < sigma(k)/k < 3 for all numbers m < k such that sigma(m)/m < 3.

1, 2, 4, 6, 12, 24, 36, 48, 60, 168, 252, 300, 336, 630, 2268, 2310, 5472, 6804, 20412, 47424, 61236, 161304, 183708, 486096, 551124, 1215216, 1653372, 4081104, 4960116, 14880348, 44641044, 133923132, 401769396, 1205308188, 1631268870, 3615924564, 10847773692

Offset: 1

Author

Amiram Eldar, Mar 26 2019

Keywords

• nonn

Comments

Analogous to A259312 with 3-deficient numbers instead of 3-abundant numbers.

Analogous to A228450 with ratio 3 instead of 2.

The values of sigma(a(n))/a(n) are 1, 1.5, 1.75, 2, 2.333..., 2.5, 2.527..., 2.583..., 2.8, ...

Crossrefs

Cf. A071927, A023197, A228450, A259312.

Programs

Mathematica

sm=0; seq={}; Do[s=DivisorSigma[1,n]/n; If[s<3 && s>sm, sm=s; AppendTo[seq, n]], {n,1,100000}]; seq