Designing 64.5kHz Hartley Oscillator
As with the colpitts oscillator an extra resistor is needed. This colpitts oscillator correctly has a 200 ohm resistor (R3) in series with the op-amp output. But it can be a few ohms to a kohm mainly: -



If that resistor is not present the very low output impedance of the op-amp will prevent enough phase shift occuring to cause predictable sustained oscillation. With a Hartley you have the same issue: -



If you don't have that resistor it may oscillate but at the wrong frequency and only because of the delay through the op-amp is akin to adding phase shift. Here's the proof that for a BJT common collector colpitts oscillator you need "R" to get the right phase shift and this is exactly the same for a Hartley oscillator: -



One final note - the Hartley oscillator DOES NOT need to have a coupled inductor despite what other have said.

And that "extra" resistor is also needed in Pierce crytal oscillators for precisely the same reason: -



The resistor I'm talking about is R1 above - it adds extra phase shift that takes the overall phase shift past the 180 degrees point therefore there will always be a frequency where precisely 180 degrees is formed and this is the frequency that the oscillator will run at.

This question and my answer show how the phase shift may not be quite enough without the series resistor feeding capacitor C1 and the crystal.