SPECIAL NUMBERS

SMITH NUMBER :- COMPOUND NUMBER IN WHICH SUM OF THE DIGITS IS EQUAL TO SUM OF THE DIGITS IN ITS PRIME FACTORS. Example:- 690

In 690 sum of digits 6+9+0=15

Prime factors of 690 = 2 X 3 X 5 X 23 

sum of the digits in its factors = 2 + 3 + 5 + 2 + 3 = 15

ABSOLUTE PRIME NUMBER :- PRIME Number in which numbers formed due to interchange of places are all Prime numbers.

Example:- 113

Numbers formed due to interchange of places :- 311 , 131

113, 311, 131 are prime numbers. 

Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number. 

For example, the smallest pair of amicable numbers is (220, 284); for the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.

The first few amicable pairs are: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368)

1729  -----> SRINIVASA RAMANUJAN NUMBER :- Least number that can be expressed in sum of two cubes in two different ways. 

Betrothed numbers or quasi-amicable numbers are two positive integers such that the sum of the proper divisors of either number is one more than the value of the other number. In other words, (m, n) are a pair of betrothed numbers if s(m) = n + 1 and s(n) = m + 1, where s(n) is the aliquot sum of n.

The first few pairs of betrothed numbers are: (48, 75), (140, 195), (1050, 1575), (1648, 1925)