Template:Sequence of the Day for August 26

Intended for: August 26, 2011

Timetable

• First draft entered by Alonso del Arte on August 25, 2011 ✓
• Draft reviewed by AL on August 25, 2011 ✓
• Draft to be approved by July 26, 2011

Yesterday's SOTD * Tomorrow's SOTD

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A064510: Numbers

n

such that the sum of the first

k

divisors of

n

is equal to

n

for some

k

.*

{ 1, 6, 24, 28, 496, 2016, 8128, 8190, ... }

Obviously all perfect numbers are included in this sequence, and no deficient numbers are. But if you take the perfect numbers out, you have the Erdős–Nicolas numbers left, which are a subset of the abundant numbers.

_______________

* This suggests a similar sequence: A?????? Numbers

n

such that the sum of the first

k

divisors of

n

is equal to a positive integer multiple of

n

for some

k

. (This sequence would include all perfect numbers as well as all multiperfect numbers. It would include more than the Erdős–Nicolas numbers.)