In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).
Keeping this in view, what is a happy number?
Happy number. A happy number is defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits in base-ten, and repeat the process until the number either equals 1 (where it will stay), or it loops endlessly in a cycle that does not include 1.
What is meant by Adam Number?
Adam Number. Adam number is a number when reversed, the square of the number and the square of the reversed number should be numbers which are reverse of each other. Adam numbers upto 1000 are: 0, 1, 2, 3, 11, 12, 13, 21, 22, 31, 101, 102, 103, 111, 112 , 113, 121, 122, 201, 202, 211, 212, 221, 301, 311.
What are the Armstrong numbers?
An Armstrong number of three digits is an integer such that the sum of the cubes of its digits is equal to the number itself. For example, 371 is an Armstrong number since 3**3 + 7**3 + 1**3 = 371. Write a program to find all Armstrong number in the range of 0 and 999.
What is the best number in the world?
“73 is the 21st prime number,” Sheldon explains. “Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3 and in binary 73 is a palindrome, 1001001, which backwards is 1001001.”
What is perfect number give example?
Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128.
List of perfect numbers
WHY IS 496 a perfect number?
Also related to its being a perfect number, 496 is a harmonic divisor number, since the number of proper divisors of 496 divided by the sum of the reciprocals of its divisors, 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496, (the harmonic mean), yields an integer, 5 in this case. It is the largest happy number less than 500.
What is the largest perfect number?
The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. This is followed by the perfect numbers 496 and 8128. As of January 2016, 49 Mersenne primes are known, and therefore 49 even perfect numbers (the largest of which is 274207280 × (274207281 − 1) with 44,677,235 digits).
Why is 12 not a perfect number?
Numbers like 6 that equal the sum of their factors are called perfect numbers. 4 is not a perfect number because the sum of its factors (besides 4 itself), 1+2, is less than 4. Numbers like 4 are known as deficient numbers . 12 is not a perfect number because the sum of its factors, 1+2+3+4+6 is greater than 12.
Is there a perfect square for 18?
Is 18 a perfect square number? A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 18 is about 4.243. Thus, the square root of 18 is not an integer, and therefore 18 is not a square number.
What is a perfect number simple explanation?
A number is called a perfect number if by adding all the positive divisors of the number (except itself), the result is the number itself. 6 is the first perfect number. Its divisors (other than the number itself: 6) are 1, 2, and 3 and 1 + 2 + 3 equals 6. Other perfect numbers include 28, 496 and 8128.
What is meant by narcissistic number?
In recreational number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number (after Michael F. Armstrong) or a plus perfect number) is a number that is the sum of its own digits each raised to the power of the number of digits.
What is a group of twelve called?
The usual ordinal form is “twelfth” but “dozenth” or “duodecimal” (from the Latin word) is also used in some contexts, particularly base-12 numeration. Similarly, a group of twelve things is usually a “dozen” but may also be referred to as a “duodecad”.
What is an abundant number?
In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16.
Can there be an odd perfect number?
Perfect numbers are positive integers that are the sum of their proper divisors. For instance, 6 is a perfect number, because the sum of its proper divisors, 1, 2, and 3 equals 6 (1 + 2 + 3 = 6). Furthermore, in the letter, Descartes was the first to reason that an odd perfect number may or may not exist.
What is the proper divisors?
A proper divisor of a positive integer is any divisor of other than itself. Thus, prime numbers have exactly one proper divisor, 1, and every other number has at least two proper divisors.
Is the number 127 a prime number?
As a Mersenne prime, 127 is related to the perfect number 8128. The next prime is 131, with which it comprises a cousin prime. Because the next odd number, 129, is a semiprime, 127 is a Chen prime. 127 is greater than the arithmetic mean of its two neighboring primes, thus it is a strong prime.
What are divisors of a number?
A divisor, or factor, is a number that divides evenly into a larger integer. It is easy to determine how many divisors a small integer (such as 6) has by simply listing out all the different ways you can multiply two numbers together to get to that integer.
What is a palindrome number?
A palindromic number or numeral palindrome is a number that remains the same when its digits are reversed. Like 16461, for example, it is “symmetrical”. The term palindromic is derived from palindrome, which refers to a word (such as rotor or racecar) whose spelling is unchanged when its letters are reversed.
What is a perfect number in C?
This C Program checks whether a given number is perfect number. Perfect number is a number which is equal to sum of its divisor. For eg,divisors of 6 are 1,2 and 3. The sum of these divisors is 6. The C program is successfully compiled and run on a Linux system.
What is a twin prime number?
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. However, it is unknown if there are infinitely many twin primes or if there is a largest pair.
Is the number 1 a perfect square?
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, √9 = 3, so 9 is a square number. A positive integer that has no perfect square divisors except 1 is called square-free.
What is meant by amicable numbers?
Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number. (A proper divisor of a number is a positive factor of that number other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.)