What is the sum of the even numbers between 1 and 9?
Amicable numbers period 1. Numbers that are members of an aliquot sequence with period greater than 2 are known as sociable numbers. The smallest pair of amicable numbers is (220, 284). They are amicable because 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 ten amicable pairs are: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368), (10744, 10856), (12285, 14595), (17296, 18416), (63020, 76084),
Sum and Product Puzzle need for any advanced knowledge like Goldbach’s conjecture or the fact that for the product "B·C" of such a 2-split to be unique (i.e. there are no other two numbers that also when multiplied yield the same result). But if you know Goldbach’s conjecture, though, your work is cut in half since you know immediately that the sum x+y cannot be even, since every even number can be written as the sum of two prime numbers. The product of those two numbers would then be immediately possible to factorise uniquely by the property of prime numbers. Step 1. S (Sue),