Some helpful links:

• Mathworld
• The On-Line Encyclopedia of Integer Sequences
• PARI/GP computer algebra system

Specific to this problem:

• Divisor function
• Sloane A000005
• Math::Pari

Those sites help me solve pretty much all the Project Euler problems. Of course, it does help to have some familiarity with the basics of number theory and combinatorics. Google and Wikipedia can help you with that too.

Here's my solution (runs in about 0.6 sec):