Two numbers are amicable or “friendly” if each is equal to the sum of the natural number divisors of the other. This is excluding the numbers themselves. The first pair of amicable numbers, (220 & 284) are said to have[…]

# Category: Advanced Number Curiosities

## Harshad Numbers

- LOCATED IN Advanced Number Curiosities

In recreational mathematics, a Harshad number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. For example take the number 312. The sum of its digits equal 3 + 1 +[…]

## Kaprekar’s Process

- LOCATED IN Advanced Number Curiosities

The Kaprekar process was named for the well-known Indian mathematician D.R. Kaprekar and focuses on four-digit numbers which are very unique. Take any four-digit number, (make sure that not all digits are the same) and arrange its digits in both[…]

## Perfect Numbers

- LOCATED IN Advanced Number Curiosities

A perfect number is one that is equal to the sum of its proper divisors, (please note- this does not include the perfect number itself). The first perfect number is 6. The proper divisors of 6 are 1, 2 &[…]

## Kaprekar Numbers

- LOCATED IN Advanced Number Curiosities

A Kaprekar number is a non-negative integer, whose square in that base can be split into two parts that add up to the original number again. Consider the number 45, squaring it, 452 = 2025 Now, notice that the digits in the[…]

## Narcissistic Numbers

- LOCATED IN Advanced Number Curiosities

A number is narcissistic if it equals the sum of each of its component digits raised to the same power. Note: all single digit numbers are trivial examples. The smallest number that is narcissistic is 153: 13 + 53 +[…]

## Munchhausen Numbers

- LOCATED IN Advanced Number Curiosities

A Munchhausen Number is when a digit is not raised to the same power, the case of narcissistic numbers, but raised to the power of its digit value. The single digits 0 & 1 are trivial Munchhausen Numbers. Consider the[…]

## Ruth – Aaron Pairs

- LOCATED IN Advanced Number Curiosities

A Ruth-Aaron pair are consecutive numbers whose sum of their prime factors, (multiples not counted) are equal. Their name is unique, so is their story. The smallest pair are 5 & 6 5 = 5 Sum of prime factors =[…]

## Vampire Numbers

- LOCATED IN Advanced Number Curiosities

A vampire number’s digits can be rearranged to form a product of equal value. For example: 1260 is a Vampire number as 1260 = 21 x 60. The numbers 21 and 60 in this case are called “fangs”! The number[…]

## Unique Numbers

- LOCATED IN Advanced Number Curiosities

Consider a two-digit number which contains consecutive ascending digits. For example the number 67. If we reverse these digits we have the number 76. When we find the difference between them, we obtain a value of 9. This is in[…]

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