Sum of Proper Divisors — Level 3

Inside the clockwork city of Mechania, where gears turn to the rhythm of algorithms, a young inventor named Tinker adjusts her brass goggles. The city's Great Engine is faltering, and the council has issued a Syntax Surfer decree: whoever can solve the problem "Sum of Proper Divisors — Level 3" will be granted the rank of Master Machinist. Tinker's workshop is filled with springs, cogs, and half-finished automata. The Great Engine's failure threatens to halt the city's clocks, and time itself may stop if she cannot write the right code. Read a positive integer and print the sum of its proper divisors. The engineering schematics impose the following tolerances and constraints: 1 <= n <= 10^5 The council has provided these calibration cases to ensure the Engine runs true: Input: 12 Output: 16 The mechanical pendulum swings lower with each passing minute. Tinker's soldering iron glows red. She needs a solution that fits the constraints like a perfectly machined gear. Tighten the bolts, wind the mainspring, and make the Engine sing. The path to mastering Sum of Proper Divisors — Level 3 is not one that can be walked in a single step. It demands patience, precision, and a deep respect for the boundaries that shape the problem. Many adventurers before you have attempted this trial and failed, their code crashing against the very constraints that the elders inscribed. But you have the tools. You have the training. You have reached the Syntax Surfer tier, and that alone means the council believes in your potential. Look once more at the examples above. Trace the logic with your finger if you must. Consider the time and memory limits carefully, for they are not suggestions but strict laws of the arena. When you are ready, commit your solution. Let the compiler run. Let the test cases judge your work. If your code is true, the gates will open and you will move closer to the ultimate rank. If not, study the failure, sharpen your algorithm, and try again. For in the halls of CodeTikki, the only thing more important than success is the wisdom gained from the attempt. Remember that the Syntax Surfer challenge is designed to test not just knowledge, but character. Every edge case is a lesson. Every time limit is a teacher. Every hidden test is a guardian at the gate. Do not rush. Let your code breathe. Let it be as clean as a mountain stream. When the final test passes, you will know that you have earned the title. Until then, code with courage, test with care, and never stop learning.