On positive integers \(n\) dividing the \(n\)th term of an elliptic divisibility sequence (Q713042)

Let \(E\) be an elliptic curve defined over \(\mathbb{Q}\) and suppose \(P=(x(P),y(P))\) denotes a point of infinite order. For any non-zero integer \(n\), write \[ x(nP)=\frac{A_{n}}{B_{n}} \] in lowest terms, with \(A_{n}\in\mathbb{Z}\) and \(B_{n}\in\mathbb{N}\). The sequence \((B_{n})_{n\geq 1}\) have become known as elliptic divisibility sequence. \textit{J. H. Silverman} and \textit{K. E. Stange} [Acta Arith. 146, No. 4, 355--378 (2011; Zbl 1225.11079)] studied terms in elliptic divisibility sequences divisible by their indices. In the present paper, the author discuss the distribution of these terms.