SOLUTION: A proper divisor of a positive integer is a positive integral divisor other than 1 and itself. A positive integer greater than 1 is a sweet # if the product of its distinct proper
Algebra.Com
Question 914653: A proper divisor of a positive integer is a positive integral divisor other than 1 and itself. A positive integer greater than 1 is a sweet # if the product of its distinct proper divisors is equal to the # itself. List the 10 smallest sweet numbers.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Suppose the proper divisors of n are 
where 
. Then we have 
, 
, and so on. We want the product of the d_i's to equal n, and this occurs if and only if n has two proper divisors (excluding 1), or when n has exactly four divisors. This occurs if and only if n is a product of two different primes, or n is the cube of a prime.
First 10 sweet numbers: 6, 8, 10, 14, 15, 21, 22, 26, 27, 33
RELATED QUESTIONS
How many positive integers have exactly 3 proper divisors, each of which is less than 50? (answered by Edwin McCravy,CarlosOrtiz)
What is the smallest positive integer which, when divided by each of 2, 3, 4, 5, 6
and... (answered by greenestamps)
A “simple square” is any integer greater than 1 that has only three positive integer... (answered by Edwin McCravy,CharlesG2)
If a positive integral divisor of 16200 is selected of random,given that it is even,the... (answered by KMST)
Find the biggest positive integral value that CANNOT be written as the sum of a positive... (answered by CubeyThePenguin,ikleyn)
How many positive integers n are there such that 2n+1 is a divisor of... (answered by ikleyn,greenestamps)
What is the value of the positive integer n for which the least common multiple of
36... (answered by Edwin McCravy)
What is the smallest positive divisor greater than 1 of a composite number X from the... (answered by ikleyn)
A prime number is a positive integer greater than 1 divisible by only 1 and
itself. How... (answered by Fombitz)