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MathNet 2015-part-01 — 191 problems (EN–VI) Question 86

Math Olympiad Vault · MathNet 2015-part-01 — 191 problems (EN–VI)

Question 86

A sequence is called $N$-nice if it consists of a finite number of the consecutive positive integers and the sum of all its terms is equal to $N$.
Find the total number of all $4030^k$-nice sequences, where $k$ is a positive integer. ($N$-nice sequence may consist of a single term.)