A Hardy-Ramanujan number is a number which can be expressed as the sum of two positive cubes in exactly two different ways. For example, 1729 is equal to the sum:
- or alternatively, to the sum:
- but not to any other sums of positive cubes. Let's think about a general strategy for collecting the first n of these numbers. You will need to store the numbers in an extendable data structure, such as a list. You will also need to keep trying to find numbers until you have found n of them, appending valid Hardy-Ramanujan numbers to the list as you go. To implement this, you could do a while loop which keeps looking for Hardy-Ramanujan numbers until the length of the list is n. Does that make sense?
To find the numbers themselves, you could always try the naive approach: beginning with 1729, check each number. Subtract successive integer cubes from the number and see if the difference is a cube. This could be represented by a for loop nested inside your while loop. During the for loop, keep track of every time the difference is a cube. If, when the for loop completes, the difference has been a cube only twice, you know that the number is a Hardy-Ramanujan number, and can be added to the list.
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