Given an integer N, the task is to find the Nth Mosaic number. A Mosaic number can be expressed as follows:
If N = Aa * Bb * Cc … where A, B, C.. are the prime factors of N then the Nth Mosaic number will be A * a * B * b * C * c ….
Input: N = 8
8 can be expressed as 23.
So, the 8th Mosaic number will be 2 * 3 = 6
Input: N = 36
36 can be expressed as 22 * 32.
2 * 2 * 3 * 2 = 24
Approach: We have to find all the prime factors and also the powers of the factors in the number by dividing the number by the factor until the factor divides the number. The Nth Mosaic number will then be the product of the found prime factors and their powers.
Below is the implementation of the above approach:
- Print first N Mosaic numbers
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- Find the total number of composite factor for a given number
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- Find the number of integers x in range (1,N) for which x and x+1 have same number of divisors
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- Find count of digits in a number that divide the number
- Find the maximum number of composite summands of a number
- Find M-th number whose repeated sum of digits of a number is N
- Find if a number is divisible by every number in a list
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