Recently in Topcoder, I faced a problem which stated as follows: "You have a text document, with a single character already written in it. You are allowed to perform just two operations - copy the entire text (counted as 1 step), or paste whatever is in the clipboard (counted as 1 step). When you paste whatever is there in the clipboard, the original text on the text document is appended with that on the clipboard. Copying overrites whatever there is on the cliboard. It is required to find the minimum number of steps required to print 'n' characters on the text document. For Example, to generate 9 characters - Copy the single character already present, Paste (2 chars), paste again (3 chars), copy (3 chars copied), paste (6 chars now), paste again (9 chars now). So, total number of steps required is 6 which is (3+3 sum of prime factors of 9).
Can someone tell, how is this problem related to sum of the prime factors of 'n'?