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Articles by Eva Sharma
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P-Smooth Numbers or P-friable Number
A number is p-friable for p-smooth if all of its prime factors are less than or equal to p. For example, 1620 is a 5-smooth number. Because, the prime factors of 1620 are: 2, 3, and 5. As it can be seen, 1620 is also a 7-smooth and 11-smooth number. Problem Statement Given two numbers N and P, we have to check if N is a P-friable number or not. Examples Input − N = 50, P = 7 Output − Yes, 50 is a 7-friable number. Explanation 50 can be prime factorized as: 5*5*5*5. Hence, ...
Read MorePerfect Power (1, 4, 8, 9, 16, 25, 27, ...)
A Perfect Power is a Natural Number that is the product of equal natural factors. It can also be defined as an integer that can be expressed as a square power or a higher power of another integer greater than one. For example, 4 can be expressed as the product of 2*2. 27 can be expressed as the product of 3*3*3. Hence, 4 and 27 are perfect powers. Problem Statement Given a number n, find the count of perfect numbers which are less than or equal to n. Example 1 Input = 14 Output = 3 Explanation 1 ...
Read MoreLegendre's Conjecture: Concept, Algorithm, Implementation in C++
The Legendre’s Conjecture states that at least one prime number always exists between two consecutive natural numbers' squares. Mathematically, there is always a prime number p between any two numbers n2 and (n+1)2. n is a natural number. A conjecture means a conclusion that doesn't has mathematical proof. Hence, Legendre's Conjecture is just a statement with no mathematical proof. Problem Statement For a number n, print the number of primes in the range of n2 to (n+1)2 from 1 to n. Examples Input: 4 Output: For i = 1: Total primes in the range 1 and 4 = 2 ...
Read MoreForm a Number Using Corner Digits of Powers
What are Corner digits? The corner digits of a number refer to the rightmost and the leftmost digits. For example, the corner digits of 1234 are 1 and 4. The corner digits of a single-digit number will be the number twice. For example, the corner digits of 2 will be 2 and 2. Problem Statement For given two numbers, n, and x, form a number using the corner digits of all the powers of n from 1 and x, i.e., n1, n2....nx. Examples Input: n = 2, x = 4 Output: 22448816 Explanation 21 = 2. Corner digits = ...
Read MoreDecimal Equivalent of Gray Code and Its Inverse
Gray code or reflected binary code is a form of a binary representation of numbers in which two consecutive numbers only differ by one bit. For example, the gray code of 1 is 001, while the gray code of 2 is 011. Gray code is usually used in error correction because it prevents some data errors that can happen in the usual binary representations while state changes. Gray code is also helpful in k-maps, communication, etc., because of its unique property. Prerequisite Study decimal, binary and gray code notations before reading further. Problem Statement 1 Given a decimal number n, ...
Read MoreCube Free Numbers smaller than n
Cube-free numbers are those numbers that have no cubic divisors. A cubic divisor refers to an integer that is a cube and divides the number with zero remainders. For example, 8 is a cubic divisor of 16 since 8 is a cube of 2 (2*2*2 = 8), and 8 divides 16 with the remainder of zero. Thus, 8 and 16 both are not cube-free numbers. Problem Statement Find all the cube-free numbers less than a given number, n. Example Let's understand the problem with an example. Let n = 15, Thus, we have to find all the numbers less than ...
Read MoreSquare pyramidal number (Sum of Squares)
A Square Pyramidal Number means the Sum of the Square of Natural Numbers. Natural Numbers include all the numbers from 1 to infinity. For example, the first 4 Square pyramidal numbers are 1, 5, 14, 30. For better perception, consider the fact: If we take spheres of numbers equal to the square pyramidal numbers, starting from one, and stack them in descending order, they create a pyramid. Problem Statement Given a number Sum. If Sum is the sum of the squares of first “n” natural numbers, return n, otherwise return false. Example 1 Input = 30 Output = 4 ...
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