An engineers' dream come true

Consider the number 6. The divisors of 6 are: 1,2,3 and 6. Every number from 1 up to and including 6 can be written as a sum of distinct divisors of 6: 1=1, 2=2, 3=1+2, 4=1+3, 5=2+3, 6=6. A number n is called a practical number if every number from 1 up to and including n can be expressed as a sum of distinct divisors of n.

A pair of consecutive prime numbers with a difference of six is called a sexy pair (since "sex" is the Latin word for "six"). The first sexy pair is (23, 29).

We may occasionally find a triple-pair, which means three consecutive sexy prime pairs, such that the second member of each pair is the first member of the next pair.

We shall call a number n such that :

• (n-9, n-3), (n-3,n+3), (n+3, n+9) form a triple-pair, and
• the numbers n-8, n-4, n, n+4 and n+8 are all practical,

Find the sum of the first four engineers’ paradises.

Written by gamwe6 who lives and works in San Francisco building useful things. You should follow him on Twitter