Context :

Aims : We studied the correlations between spin frequencies and kilohertz quasi-periodic oscillations ( kHz QPOs ) in neutron star low mass X-ray binaries .

Methods : The updated data of kHz QPOs and spin frequencies are statistically analyzed .

Results : We found that when two simultaneous kHz QPOs are present in the power spectrum , the minimum frequency of upper kHz QPO is at least 1.3 times larger than the spin frequency , i.e . \nu _ { s } < \nu _ { 2 min } / 1.3 .
We also found that the average kHz QPO peak separation in 6 Atoll sources anti-correlates with the spin frequency in the form \langle \Delta \nu \rangle = - ( 0.19 \pm 0.05 ) \nu _ { s } + ( 389.40 \pm 21.67 ) Hz .
If we shifted this correlation in the direction of the peak separation by a factor of 1.5 , this correlation matches the data points of the two accretion powered millisecond X-ray pulsars , SAX J1808.4-3658 and XTE J1807-294 .

Conclusions :