The conjecture that all sub-perfect numbers are powers of 2 is indeed false. A counter-example to this conjecture is 12.
To show that 12 is a sub-perfect number, let's find the sum of its divisors less than 12:
1 + 2 + 3 + 4 + 6 = 16
As the sum of its divisors less than 12 is 16, which is equal to 12 - 1, 12 qualifies as a sub-perfect number.
However, 12 is not a power of 2. Thus, 12 serves as a counter-example to the conjecture.
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