Some arithmetic functions of factorials in Lucas sequences

We prove that if {un}n≥ 0 is a nondegenerate Lucas sequence, then there are only finitely many effectively computable positive integers n such |un|=f(m!), where f either the sum-of-divisors function, or sum-of-proper-divisors Euler phi function. also give theorem holds for more general class of integer sequences and illustrate our results through few specific examples. This paper motivated by previous work Iannucci Luca who addressed above problem with Catalan numbers