Number-Theoretical Fibonacci-Like Sequence

[Ralf Stephan]

You wrote 
> I may have made a mistake in calculating terms, but this sequence does
> not yet seem to be in the EIS.
> 
> Let a(1) = a(2) = 1;
> 
> For m >= 2,
> let a(m+1) = a(m) + a(j(m)),
> 
> where j(m) is the largest PROPER divisor of m.
> 
> (I have probably over-represented this sequence by calling it
> "Fibonacci-like".)
> 
> The sequence begins (?):
> 
> 1, 1, 2, 3, 4, 5, 7, 8, 11, 13, 17, 18, 23,...
m 1  2  3  4  5  6  7  8  9   10  11  12  13
j    1  1  1  1  2  1  3  2   4   1   5
           2     3     4  3   5       9   
> 
> Is there a closed-form for the a(m)'s? 

Don't one first try to get that for j(m) before doing such things?

> 
> Thanks,
> Leroy Quet
> 
> PS: There are probably other good examples of sequences combining somehow 
> number-theory and Fibonacci numbers.
>