Homotopy type of smooth weighted complete intersections

If the total degree d has no prime divisors less than $ \tfrac{{n + 3}} {2} $ , then we prove that the homotopy type of complex odd dimensional smooth weighted complete intersection X _n (d;w) is determined by the dimension n, the total degree d, the Euler characteristic and the Kervaire invariant, provided that the weights w = (ω ₀,..., ω _{n +r} ) is pairwise relatively prime.