Primitive Abundant Number/Examples/304
Jump to navigation
Jump to search
Example of Primitive Abundant Number
$304$ is a primitive abundant number:
- $1 + 2 + 4 + 8 + 16 + 19 + 38 + 76 + 152 = 316 > 304$
Proof
From $\sigma_1$ of $304$, we have:
- $\map {\sigma_1} {304} - 304 = 316$
where $\sigma_1$ denotes the divisor sum function: the sum of all divisors of $304$.
Thus, by definition, $304$ is an abundant number.
The aliquot parts of $304$ are enumerated at $\sigma_0$ of $304$:
- $1, 2, 4, 8, 16, 19, 38, 76, 152$
By inspecting the divisor sums of each of these, they are seen to be deficient.
Hence the result, by definition of primitive abundant number.
$\blacksquare$