
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
For all  $n>1$  let  $f(n)$  be the sum of the smallest factor of  $n$  that is not 1  and  $n$  . The computer prints  $f(2),f(3),f(4),...$  with order: $4,6,6,...$  ( Because  $f(2)=2+2=4,f(3)=3+3=6,f(4)=4+2=6$  etc.). In this infinite sequence, how many times will be  $ 2015$   and  $ 2016$    written? (Explain your answer)

Present the answer in LaTex format: \boxed{Your answer}
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