## Factors

View as PDF

Points: 7
Time limit: 1.0s
Memory limit: 256M

Author:
Problem type

You are given two positive integers, and . How many factors does the sum of the integers from to inclusive have?

#### Input Specification

The input contains one line with two space-separated integers, and .

#### Output Specification

Output a single integer, the number of factors of the sum of the integers from to inclusive.

#### Constraints #### Sample Input

1 3

#### Sample Output

4

• commented on Dec. 7, 2022, 2:51 p.m.

Can anyone help me with test case 4? 48 is marked as incorrect, but I don't understand why.

The input is 1 1000000000000. The sum of the numbers in between should be 1001882602603448320. I have calculated its factors to be the following.

1, 1001882602603448320

2, 500941301301724160

4, 250470650650862080

5, 200376520520689664

8, 125235325325431040

10, 100188260260344832

16, 62617662662715520

20, 50094130130172416

32, 31308831331357760

40, 25047065065086208

64, 15654415665678880

80, 12523532532543104

128, 7827207832839440

160, 6261766266271552

256, 3913603916419720

320, 3130883133135776

512, 1956801958209860

640, 1565441566567888

1024, 978400979104930

1280, 782720783283944

2048, 489200489552465

2560, 391360391641972

5120, 195680195820986

10240, 97840097910493

This makes for 24 pairs, or 48 total individual factors. Alternatively, the number of factors can be calculated through prime numbers. I have calculated the prime factorisation of to be (2^11)(5^1)(97840097910493^1). Taking the exponents of each, you can deduce that the number of factors should be (11 + 1)(1 + 1)(1 + 1), which is equal to 48.

What am I overlooking?

• commented on Dec. 7, 2022, 4:34 p.m.

What is the sum of the first positive integers? Please show your work.

• commented on Dec. 7, 2022, 6:41 p.m.

I was using the formula y = x(x + 1)/2 on a separate program I made, but having redone the calculation separately, my program didn't get it right. Thanks.