Hey guys, I recently stumbled across this interesting sequence:


1, 3, 5, 11, 17, 39, 65, 139, 261, 531, 1025, 2095, 4097, 8259, 16405, 32907, 65537, 131367, 262145 ...


Any ideas? The sequence appears to somewhat resemble the binary sequence.



What is the pattern in this sequence of integers
I would try this: <http://oeis.org/A034729>


$$ a(n) = \sum\_{k, k|n } 2^{(k-1)}$$


In Mathematica syntax this is (see [W|A](http://www.wolframalpha.com/input/?i=Table%5BSum%5B2%5E%28k-1%29,%7Bk,Divisors%5Bn%5D%7D%5D,%7Bn,1,20%7D%5D))



```
 Sum[2^(k - 1), {k, Divisors[n]}]

```

