Category: Advanced Number Curiosities

March 21 2016

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[…]

March 22 2016

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 +[…]

March 23 2016

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[…]

March 24 2016

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 &[…]

March 25 2016

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[…]

March 26 2016

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 +[…]

March 28 2016

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[…]

March 29 2016

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 =[…]

March 30 2016

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[…]

March 31 2016

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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