A230148 Numbers whose abundancy, sigma(n)/n, is 1024/513.

397575, 3145425129, 7096702977, 53164445037705, 130468907286855, 1229923663366167, 2774951736355071

Offset: 1

Author

Michel Marcus, Oct 11 2013

Keywords

• nonn

Comments

This list of 7 numbers is conjectured to be complete.

They are mentioned in conjunction with an example of a family of 7 isotopic amicable pairs (see Example 2.4 on page 3 of the Garcia et al. link).

Start from the amicable pair (961388889147024075, 961453639626095925). It can be written as (g*m, g*n), with g=3^3*5^2*19*31=397575, with sigma(g)/g=1024/513 and GCD(g,m) = GCD(g,n) = 1. Then by replacing g any of the other 6 values of the sequence, we obtain 6 other amicable pairs, isotopic to the first one.

These numbers belong to A222263 with k = 1/512.

Examples

			For n = 397575, sigma(n)/n = 793600/397575 = 1024/513.
		

Links

• M. García, J. M. Pedersen, H. J. J. te Riele, Amicable pairs, a survey, Report MAS-R0307, Centrum Wiskunde & Informatica.

Crossrefs

Cf. A222263.