Given a number N, print all numbers in range from 1 to N having exactly 3 divisors. Input : N = 16 Output : 4 9 4 and 9 have exactly three divisors. Divisor Input : N = 49 Output : 4 9 25 49 4, 9, 25 and 49 have exactly three divisors. Recommended: Please solve it on “ PRACTICE ” first, before moving on to the solution.
Which is a divisor of the number 21?
For example, 3 is a divisor of 21, since 21/7 = 3 (and 7 is also a divisor of 21). If m is a divisor of n then so is − m. The tables below only list positive divisors. a prime number has only 1 and itself as divisors; that is, d ( n ) = 2. Prime numbers are always deficient as s ( n )=1
Which is a divisor of the number n?
The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n / m is again an integer (which is necessarily also a divisor of n ). For example, 3 is a divisor of 21, since 21/7 = 3 (and 7 is also a divisor of 21). If m is a divisor of n then so is − m.
How many divisors does a prime number have?
a prime number has only 1 and itself as divisors; that is, d ( n ) = 2. Prime numbers are always deficient as s ( n )=1 a highly composite number has more divisors than any lesser number; that is, d (n) > d (m) for every positive integer m < n.
How to calculate the number of divisors in a table?
1 to 100 n Divisors d ( n ) σ ( n ) s ( n ) 31 1, 31 2 32 1 32 1, 2, 4, 8, 16, 32 6 63 31 33 1, 3, 11, 33 4 48 15 96 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 12 252 156
Which is the third divisor of the number x?
Therefore the third divisor must be a prime number. So the three divisors of ‘x’ are: 1, p, x where p is prime. Now since p is a divisor (or factor) of x, and the only other divisor besides 1 and x itself, x must equal p*p — or x=p^2 .
Which is the smallest number with specific number of divisors?
Different divisors have different collections of powers, so the number of divisors will be ( m 1 + 1) ( m 2 + 1)… ( m k + 1). Now let’s find the smallest N such that ( m 1 + 1) ( m 2 + 1)… ( m k + 1) = 24.
