Given a range of integer from ‘a’ to ‘b’ . Our task is to calculate the amount of numbers from the interval [ a, b ], that are not divisible by any number between 2 and k – 1 and yet divisible by k .
Note : We do not have to consider a divisor equal to one.
Input : a = 12, b = 23, k = 3 Output : 2 Between [12, 23], 15 and 21 are the only number which are divisible k and not divisible by any number between 2 and k - 1. Input : a = 1, b = 80, k = 7 Output : 3
Approach : Below is the step by step algorithm to solve this problem:
- A number is divisible only by k and not by any number less than k only if k is a prime number.
- Traverse through each number from a to b to check if the number has the smallest factor as a prime number k.
- Count all such numbers in the range whose smallest factor is a prime number k.
Below is the implementation of the above approach:
- Count all the numbers less than 10^6 whose minimum prime factor is N
- Find kth smallest number in range [1, n] when all the odd numbers are deleted
- Count Odd and Even numbers in a range from L to R
- Count of numbers having only 1 set bit in the range [0, n]
- Smallest number S such that N is a factor of S factorial or S!
- Count factorial numbers in a given range
- Count numbers in range 1 to N which are divisible by X but not by Y
- Count the numbers divisible by 'M' in a given range
- Count of numbers from range [L, R] whose sum of digits is Y
- Numbers in range [L, R] such that the count of their divisors is both even and prime
- Count of common multiples of two numbers in a range
- Sum of numbers in a range [L, R] whose count of divisors is prime
- Count of Numbers in Range where the number does not contain more than K non zero digits
- Count of all even numbers in the range [L, R] whose sum of digits is divisible by 3
- Count numbers from range whose prime factors are only 2 and 3
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