P616
projecteuler.net

Creative Numbers

ℹ️Published on Saturday, 16th December 2017, 01:00 pm; Solved by 529;
Difficulty rating: 40%

Alice plays the following game, she starts with a list of integers L and on each step she can either:

  • remove two elements a and b from L and add ab to L
  • or conversely remove an element c from L that can be written as ab, with a and b being two integers such that a,b>1, and add both a and b to L

For example starting from the list L={8}, Alice can remove 8 and add 2 and 3 resulting in L={2,3} in a first step. Then she can obtain L={9} in a second step.

Note that the same integer is allowed to appear multiple times in the list.

An integer n>1 is said to be creative if for any integer m>1 Alice can obtain a list that contains m starting from L={n}.

Find the sum of all creative integers less than or equal to 1012.



Soluzione

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