Problem #PRU-109603

Problems Algebra and arithmetic Number theory. Divisibility Divisibility of a number. General properties Methods Examples and counterexamples. Constructive proofs Calculus Number sequences Number sequences (other)

Problem

Is there a sequence of natural numbers in which every natural number occurs exactly once, and for any \(k = 1, 2, 3, \dots\) the sum of the first \(k\) terms of the sequence is divisible by \(k\)?