What makes a number abundant

Gerhard Paseman gave a hint that seemed a little bit opaque to me, probably because he believed this was a homework question; I was attempting a bit more transparency. I would have been happy for a comment. I'll give you my first up vote. I will look up Erdos' proof and see if it resembles the sketch I gave above that there exists arbitrarily long sequences which do not contain a deficient number.

Show 1 more comment. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Featured on Meta. Now live: A fully responsive profile. Related 7. Question feed. MathOverflow works best with JavaScript enabled. Accept all cookies Customize settings. Its proper divisors are 1, 2, 3, 4 and 6 for a total of The amount by which the sum exceeds the number is the abundance.

Therefore, is an abundant number. Its proper divisors are 1, 3 and 7, and their sum is Because 11 is less than 21, the number 21 is deficient. Therefore, 32 is a deficient number. The four perfect numbers 6, 28, and seem to have been known from ancient times and there is no record of these discoveries.

Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, , and 8, The first few deficient numbers are 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, How many extra pebbles are added each time? Investigate the different shaped bracelets you could make from 18 different spherical beads.

How do they compare if you use 24 beads? How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction? To find the factors of a number, you have to find all the pairs of numbers that multiply together to give that number.