PUMaC 2019 · 数论（B 组） · 第 3 题

PUMaC 2019 — Number Theory (Division B) — Problem 3

Let f be a function over the natural numbers so that (a) f (1) = 1 e e 1 k (b) If n = p ...p where p , · · · , p are distinct primes, and e , · · · e are non-negative inte- 1 k 1 k 1 k e + .. + e 1 k gers, then f ( n ) = ( − 1) . 2019 ∑ ∑ Find f ( d ). i =1 d | i

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