ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
90 lines
1.8 KiB
Markdown
90 lines
1.8 KiB
Markdown
---
|
|
id: 594810f028c0303b75339acd
|
|
title: 'Abundant, deficient and perfect number classifications'
|
|
challengeType: 5
|
|
forumTopicId: 302221
|
|
dashedName: abundant-deficient-and-perfect-number-classifications
|
|
---
|
|
|
|
# --description--
|
|
|
|
These define three classifications of positive integers based on their [proper divisors](<https://rosettacode.org/wiki/Proper divisors> "Proper divisors").
|
|
|
|
Let $P(n)$ be the sum of the proper divisors of `n` where proper divisors are all positive integers `n` other than `n` itself.
|
|
|
|
If `P(n) < n` then `n` is classed as `deficient`
|
|
|
|
If `P(n) === n` then `n` is classed as `perfect`
|
|
|
|
If `P(n) > n` then `n` is classed as `abundant`
|
|
|
|
**Example**: `6` has proper divisors of `1`, `2`, and `3`. `1 + 2 + 3 = 6`, so `6` is classed as a perfect number.
|
|
|
|
# --instructions--
|
|
|
|
Implement a function that calculates how many of the integers from `1` to `20,000` (inclusive) are in each of the three classes. Output the result as an array in the following format `[deficient, perfect, abundant]`.
|
|
|
|
# --hints--
|
|
|
|
`getDPA` should be a function.
|
|
|
|
```js
|
|
assert(typeof getDPA === 'function');
|
|
```
|
|
|
|
`getDPA` should return an array.
|
|
|
|
```js
|
|
assert(Array.isArray(getDPA(100)));
|
|
```
|
|
|
|
`getDPA` return value should have a length of 3.
|
|
|
|
```js
|
|
assert(getDPA(100).length === 3);
|
|
```
|
|
|
|
`getDPA(20000)` should equal [15043, 4, 4953]
|
|
|
|
```js
|
|
assert.deepEqual(getDPA(20000), solution);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --after-user-code--
|
|
|
|
```js
|
|
const solution = [15043, 4, 4953];
|
|
```
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function getDPA(num) {
|
|
|
|
}
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
function getDPA(num) {
|
|
const dpa = [1, 0, 0];
|
|
for (let n = 2; n <= num; n += 1) {
|
|
let ds = 1;
|
|
const e = Math.sqrt(n);
|
|
for (let d = 2; d < e; d += 1) {
|
|
if (n % d === 0) {
|
|
ds += d + (n / d);
|
|
}
|
|
}
|
|
if (n % e === 0) {
|
|
ds += e;
|
|
}
|
|
dpa[ds < n ? 0 : ds === n ? 1 : 2] += 1;
|
|
}
|
|
return dpa;
|
|
}
|
|
```
|