Given Q queries. Each query contain a positive integer n. The task is to output the sum of sum of odd number digit contained in all the divisors of n.
Input : Q = 2, n1 = 10, n2 = 36
Output : 7 18
Divisors of 10 are 1, 2, 5, 10.
Sum of odd digits in 1 is 1, in 2 is 0, in 5 is 5, in 10 is 1.
So, sum became 7.
For Query 2,
Divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
Sum of odd digits in 1 is 1, in 2 is 0, in 3 is 3, in 4 is 0,
in 6 is 0, in 9 is 9, in 12 is 1, in 18 is 1, in 36 is 3.
So, sum became 18.
The idea is to precompute the sum of odd number digit of all the numbers. Also, we can you use the sum of odd number digit of the previous number to compute the sum of odd number digit of the current number.
For example, to compute the sum of odd number digit of “123”, we can use the sum of odd number digit of “12” and “3”. Therefore, the sum of odd digit of “123” = sum of odd digit of “12” + add the last digit if it is odd (i.e 3).
Now, to find the sum of the sum of odd number digit of the factors, we can you use the jump phenomenon of Sieve of Eratosthenes. So, for all possible factors, add their contribution to its multiples.
For example, for 1 as the factor, add 1 (because 1 have only 1 odd digit) to all of its multiple.
for 2 as the factor, add 0 to all the multiples of 2 i.e 2, 4, 8, …
for 3 as the factor, add 1 to all the multiples of 3 i.e 3, 6, 9, …..
Below is the implementation of this approach:
- Queries to find whether a number has exactly four distinct factors or not
- Queries for the smallest and the largest prime number of given digit
- Number of factors of very large number N modulo M where M is any prime number
- Find number of factors of N when location of its two factors whose product is N is given
- Number which has the maximum number of distinct prime factors in the range M to N
- Super Ugly Number (Number whose prime factors are in given set)
- Number with maximum number of prime factors
- Count of Numbers in Range where first digit is equal to last digit of the number
- Number of times a number can be replaced by the sum of its digits until it only contains one digit
- Find the remainder when First digit of a number is divided by its Last digit
- Count the number of occurrences of a particular digit in a number
- Largest number less than N whose each digit is prime number
- Largest number less than N with digit sum greater than the digit sum of N
- Count number of ordered pairs with Even and Odd Sums
- Sum of all the factors of a number
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