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Rich Love, Carnation Software. 2022
Arithmetic numbers
Definition
A positive integer n is an arithmetic number if the average of its positive divisors is also an integer.
Clearly all odd primes p must be arithmetic numbers because their only divisors are 1 and p whose sum is even and hence their average must be an integer. However, the prime number 2 is not an arithmetic number because the average of its divisors is 1.5.
Example
30 is an arithmetic number because its 7 divisors are: [1, 2, 3, 5, 6, 10, 15, 30], their sum is 72 and average 9 which is an integer.
Task
Calculate and show here:
1. The first 100 arithmetic numbers.
2. The xth arithmetic number where x = 1,000 and x = 10,000.
3. How many of the first x arithmetic numbers are composite.
Note that, technically, the arithmetic number 1 is neither prime nor composite.
Stretch
Carry out the same exercise in 2. and 3. above for x = 100,000 and x = 1,000,000.
==Adding Code==
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