The overtones of two notes a perfect fifth apart do not line up, as already the perfect fifth itself is not an overtone of the base tone. This is indeed the cas

The overtones of two notes a perfect fifth apart do not line up, as already the perfect fifth itself is not an overtone of the base tone. This is indeed the case for the octave+fifth, but there you've got already clearly a second order, as it's exactly 3 times the frequency of the base while the octave is 2 times the base frequency.