Search results
Results from the WOW.Com Content Network
The number of perfect numbers less than n is less than , where c > 0 is a constant. [53] In fact it is (), using little-o notation. [54] Every even perfect number ends in 6 or 28, base ten; and, with the only exception of 6, ends in 1 in base 9.
Perfect numbers are natural numbers that equal the sum of their positive proper divisors, which are divisors excluding the number itself. So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. [2] [4] Euclid proved c. 300 BCE that every Mersenne prime M p = 2 p − 1 has a corresponding perfect number M p ...
The following program in Python determines whether an integer number is a Munchausen Number / Perfect Digit to Digit Invariant or not, following the convention =. num = int ( input ( "Enter number:" )) temp = num s = 0.0 while num > 0 : digit = num % 10 num //= 10 s += pow ( digit , digit ) if s == temp : print ( "Munchausen Number" ) else ...
A perfect number is a natural number that equals the sum of its proper divisors, the numbers that are less than it and divide it evenly (with remainder zero). For instance, the proper divisors of 6 are 1, 2, and 3, which sum to 6, so 6 is perfect. A Mersenne prime is a prime number of the form M p = 2 p − 1, one less than a power of two.
A perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers; if the sum equals n, then n is a perfect totient number.
In number theory, a narcissistic number [1] [2] (also known as a pluperfect digital invariant (PPDI), [3] an Armstrong number [4] (after Michael F. Armstrong) [5] or a plus perfect number) [6] in a given number base is a number that is the sum of its own digits each raised to the power of the number of digits.
Notably, absent consensus, please do not add articles about individual perfect numbers themselves (such as 6). Pages in category "Perfect numbers" The following 11 pages are in this category, out of 11 total.
A number that is k-perfect for a certain k is called a multiply perfect number. As of 2014, k-perfect numbers are known for each value of k up to 11. [1] It is unknown whether there are any odd multiply perfect numbers other than 1. The first few multiply perfect numbers are: