ABA12D - Sum of divisors!
Note: If you really want to learn something by solving this problem, don't hard code! There is a nice logic behind this!
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Kartheeswaran was recently reading an article on perfect numbers, whose sum of divisors equals twice the number. He was intrigued by them and decided to generate them but to his disappointment they turned out to be quite rare. So he decided to look out for a different property related to sum of divisors. What is more interesting than a number being a prime? So he decided to look out for numbers whose sum of divisors is a prime number and he was the inventor of these special numbers he gave them the name K-numbers.
Given a range [A, B] you are expected to find the number of K-numbers in this range.
Input
The first line of input indicates the number of test cases T. Then in the following T lines there will be a pair of integers A and B.
Output
Output T lines each containing a single integer ‘c’ which denotes the number of K-numbers which lie in the interval [A, B] inclusive of the end points.
Constraints
1 <= T <= 10000
1<=A<=B<=10^6
Example
Input: 2 1 5 9 10 Output: 2 1
Explanation of Sample
1) In the range [1, 5] the K-numbers are 2 and 4 because divisors of 2 are 1 and 2 which sum up to 3, which is a prime. Divisors of 4 are 1, 2 and 4 which sum up to 7, which is a prime.
2) The only K-number in the range [9, 10] is 9.
hide comments
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lone_coderrr:
2020-06-26 17:28:13
Easy peasy, 0.02 AC! |
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sarthak_19:
2019-10-28 03:54:04
nice logic :) |
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prudhvi_495:
2019-05-11 20:44:09
My 100th ^..^ |
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kspoj:
2017-11-30 09:21:22
hardcoded :( |
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sahil070197:
2017-11-24 09:21:34
It's really nice :)
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sonudoo:
2017-06-15 16:24:43
I factorized only the numbers which are perfect squares. There has to be a better way to solve this.. |
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tusharuppal:
2017-06-14 11:43:50
easy one...AC in one go ;-) |
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adm2215:
2017-04-10 19:55:17
Implemented brute force approach but got TLE , eventually hard coded . ;(( |
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amulyagaur:
2017-03-16 10:24:54
https://oeis.org/A023194 |
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cake_is_a_lie:
2017-03-06 02:49:13
Rather than say "If you really want to learn something by solving this problem, don't hard code!", you might as well have increased the time limit to ~3s and the query limit to 10^12; that would have made hard-coding without the proper solution impractical. |
| Added by: | Kashyap Krishnakumar |
| Date: | 2012-01-13 |
| Time limit: | 0.103s |
| Source limit: | 50000B |
| Memory limit: | 1536MB |
| Cluster: | Cube (Intel G860) |
| Languages: | All except: ASM32-GCC ASM64 MAWK BC C-CLANG NCSHARP CPP14 CPP14-CLANG COBOL COFFEE D-CLANG D-DMD DART ELIXIR FANTOM FORTH GOSU GRV JS-MONKEY JULIA KTLN NIM NODEJS OBJC OBJC-CLANG OCT PICO PROLOG PYPY PYPY3 PY_NBC R RACKET RUST CHICKEN SQLITE SWIFT UNLAMBDA VB.NET |
| Resource: | Own problem |
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