We Draw a graph to represent how are acting the multiples:

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s(n): It’s the sum of divisors up to n including n.
s(n): It’s the sum of divisors up to n, not including n. It’s s(n)-n.

    • si s(n)=1 the number is prime.

    • si s(n)<n the number is deficient.

    • si s(n)=n the number is perfect.

    • si s(n)>n the number is abundant.

Based on the proposed E.Pol Omar and programmed by Jason-Davies.
Are you able to detect a pattern to the prime numbers?

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