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)

14–16 5.0

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 $k$ ?

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