random integer properties?

[wigianto]

so what's with all these "which of the following i a(n): economical, wasteful, frugal, equidigital number" questions?

aka what do all those words mean, and what other have you guys seen on these tests?

[Quelloquialism]

MathWorld is an excellent place to find out more about these annoying little problems. =)

MathWorld links:










Wikipedia links:









It's likely that I'm leaving some number classes out, as I've always found studying these to be significantly less interesting than most other problems on the test. Anybody else know of some?

Edit: List updated to include Wikipedia links and the Abundant/Perfect/Deficient classes; thanks, fishslap!

Interestingly, while hunting for number types, it seems that Wikipedia and MathWorld do not agree on something...MathWorld describes frugal numbers as non-wasteful numbers (= equidigital + economical), but Wikipedia describes frugal as non-wasteful and non-equidigital, but does not mention "economical" at all. Peculiar...or maybe I'm misreading? I only glanced at it briefly, so I probably did.

[fishslap]

From what I can figure out they're just other types of numbers. Sort of like how there's prime numbers, odd numbers, even numbers, etc.

The most common ones I've seen are abundant, deficient, perfect and lucky numbers. I just look these sort of questions up on Wikipedia and somehow remember it for a test.

[edit: Quelloquialism beat me!]

[Quelloquialism]

Oh, I forgot the ones that I actually do know, haha:

Deficient numbers are greater than the sum of their proper positive integral divisors; perfect numbers are equal to the sum of their proper positive integral divisors; abundant numbers are less than the sum of their proper positive integral divisors.

The best way to approach these three types, I think, are to memorize a few key numbers and learn a few key concepts:

a) There are only three perfect numbers under 1000; they are 6, 28, and 496.
b) All multiples of perfect numbers are abundant.
c) There are only fourteen abundant numbers under 1000 which cannot be derived from rules a) and b); they are 20, 70, 88, 104, 272, 304, 368, 464, 550, 572, 650, 748, 836, and 945.
d) All multiples of abundant numbers are abundant.

Really, I don't think you'd have to memorize even that many, at least for those abundants in part c)...I wouldn't know how far the tests go, though, because I've never bothered to look too much into it.

I think the only way I'll force myself to remember these is to make a program for generating and analyzing them. That's the only reason I can remember Abundant/Deficient/Perfect, when it was brought up a long time ago in the days when Texasmath used a Bravenet forum.

[AuSmith]