Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1993. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 21)

Bui Minh Phong: Recurrence sequences and pseudoprimes

A natural number m is called weakly composite if the reciprocal sum of its distinct prime divisors is not greater than 2, i.e. V\m P Proving conjecture of I. Kätai, J. Galambos (Proc. Amer. Math. Soc. 29, 1986, 215—216) showed that for any sufficiently large n there is a weakly composite number between n and « + log log log«. In [10] (Chapter 4, Theorem 4.2) we proved Theorem 1.4. ([10]) Let U = U(L,M) be a non-degenerate Lehmer sequence. For any n > 3 there is a Lehmer number U

m such that p\u

m P and n < m < n + log log n, where C is a constant depending only on L and M. We note that this result is an extension of result of P. Kiss and B. M. Phong [13] who proved a similar estimation for a non-degenerate Lucas sequence. 117