(adsbygoogle = window.adsbygoogle || []).push({}); 90 - The Only "Deficiently Perfect Imperfect Number" ?

A125310 Numbers n such that n = sum of deficient proper divisors of n.

6, 28,90, 496, 8128, 33550336

http://oeis.org/A125310

Joseph Pe offers the following comments:

COMMENTS 1. Since any proper divisor of an even perfect number is deficient, all even perfect numbers are (trivially) included in the sequence. 2. Hence the interesting terms of the sequence are its non-perfect terms, which I call "deficiently perfect". 90 is the only such term < 10^8.

And concludes with the following question:

"Are there any more?"

It's a question I share and I'm curious if anyone would care to extend the lower bound on this implied conjecture via brute force or offer a way to prove (or disprove) it outright and/or specify conditions such an integer would have to fulfill (such as, for instance, being abundant...)

TIA,

AC

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# 90 - The Only Deficiently Perfect Imperfect Number ?

**Physics Forums | Science Articles, Homework Help, Discussion**