# Definition:Primitive Semiperfect Number

## Definition

A primitive semiperfect number is a semiperfect number which is not a multiple of a smaller semiperfect number.

### Sequence of Primitive Semiperfect Numbers

The sequence of primitive semiperfect numbers begins:

$6, 20, 28, 88, 104, 272, 304, 350, 368, 464, 490, 496, 550, 572, \ldots$

## Examples

### 6

$6$ is a primitive semiperfect number:

$1 + 2 + 3 = 6$

### 20

$20$ is a primitive semiperfect number:

$1 + 4 + 5 + 10 = 20$

### 28

$28$ is a primitive semiperfect number:

$1 + 2 + 4 + 7 + 14 = 28$

### 88

$88$ is a primitive semiperfect number:

$1 + 2 + 8 + 11 + 22 + 44 = 88$

### 104

$104$ is a primitive semiperfect number:

$1 + 4 + 8 + 13 + 26 + 52 = 104$

### 272

$272$ is a primitive semiperfect number:

$1 + 16 + 17 + 34 + 68 + 136 = 272$

and so on.

## Also known as

A primitive semiperfect number is also known as:

a primitive pseudoperfect number
an irreducible pseudoperfect number
an irreducible semiperfect number

Semiperfect can also be seen hyphenated: semi-perfect.