We use N -body simulations to measure mass functions in flat cosmological models with quintessence characterized by constant w with w = -1 , -2 / 3 
and -1 / 2 .
The results are compared to the predictions of the formula proposed by Jenkins et al .
at different redshifts , in terms of FOF masses as well as Abell masses appropriate for direct comparison to observations .
The formula reproduces quite well the mass functions of simulated haloes in models with quintessence .
We use the cluster mass function data at a number of redshifts from Carlberg et al .
to constrain \Omega _ { 0 } , \sigma _ { 8 } and w .
The best fit is obtained in the limit w \rightarrow 0 , but none of the values of w in the considered range -1 \leq w < 0 can actually be excluded .
However , the adopted value of w affects significantly the constraints in the \Omega _ { 0 } - \sigma _ { 8 } plane .
Taking into account the dependence on w we find \Omega _ { 0 } = 0.32 \pm 0.15 and \sigma _ { 8 } = 0.85 _ { -0.12 } ^ { +0.38 } ( 68 \% c.l . ) .
Since less negative w push the confidence regions toward higher \Omega _ { 0 } and lower \sigma _ { 8 } we conclude that relaxing the assumption of w = -1 typically made in such comparisons may resolve the discrepancy between recent cluster mass function results ( yielding rather low \Omega _ { 0 } and high \sigma _ { 8 } ) and most other estimates .
The fact that high w values are preferred may however also point towards some unknown systematics in the data or the model with constant w being inadequate .