Terms in elliptic divisibility sequences divisible by their indices

Abstract. Let D = (Dn)n≥1 be an elliptic divisibility sequence. We study the set S(D) of indices n satisfying n | Dn. In particular, given an index n ∈ S(D), we explain how to construct elements nd ∈ S(D), where d is either a prime divisor of Dn, or d is the product of the primes in an aliquot cycle for D. We also give bounds for the exceptional indices that are not constructed in this way