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
Comments
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 be1001882602603448320
. 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?
What is the sum of the first
positive integers? Please show your work.
I was using the formula
on a separate program I made, but having redone the calculation separately, my program didn't get it right. Thanks.
I am at the same place where you were before. But how did you get out?
In test case 4,
,
, I got sum(A,B) = 1001882602603448320. and the answer is 48.
Thanks.