45 lines
		
	
	
		
			729 B
		
	
	
	
		
			Markdown
		
	
	
	
	
	
		
		
			
		
	
	
			45 lines
		
	
	
		
			729 B
		
	
	
	
		
			Markdown
		
	
	
	
	
	
| 
								 | 
							
								---
							 | 
						||
| 
								 | 
							
								id: 5900f4e81000cf542c50fffa
							 | 
						||
| 
								 | 
							
								title: 'Problem 379: Least common multiple count'
							 | 
						||
| 
								 | 
							
								challengeType: 5
							 | 
						||
| 
								 | 
							
								forumTopicId: 302041
							 | 
						||
| 
								 | 
							
								dashedName: problem-379-least-common-multiple-count
							 | 
						||
| 
								 | 
							
								---
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								# --description--
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								Let f(n) be the number of couples (x,y) with x and y positive integers, x ≤ y and the least common multiple of x and y equal to n.
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								Let g be the summatory function of f, i.e.: g(n) = ∑ f(i) for 1 ≤ i ≤ n.
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								You are given that g(106) = 37429395.
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								Find g(1012).
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								# --hints--
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								`euler379()` should return 132314136838185.
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								```js
							 | 
						||
| 
								 | 
							
								assert.strictEqual(euler379(), 132314136838185);
							 | 
						||
| 
								 | 
							
								```
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								# --seed--
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								## --seed-contents--
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								```js
							 | 
						||
| 
								 | 
							
								function euler379() {
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								  return true;
							 | 
						||
| 
								 | 
							
								}
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								euler379();
							 | 
						||
| 
								 | 
							
								```
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								# --solutions--
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								```js
							 | 
						||
| 
								 | 
							
								// solution required
							 | 
						||
| 
								 | 
							
								```
							 |