Almost Perfect Number
An almost perfect number, also known as a least deficient or slightly defective (Singh 1997) number, is a positive integer 
for which the divisor function satisfies 
. The
only known almost perfect numbers are the powers of 2,
namely 1, 2, 4, 8, 16, 32, ... (Sloane's A000079).
It seems to be an open problem to show that a number is almost perfect only if it is of the form 
.
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(3+(1-sqrt(2))/(1+sqrt(2)))^(1/3)