ホーム - Project Euler

Problem 21¶

Amicable Numbers¶

Let $d(n)$ be defined as the sum of proper divisors of $n$ (numbers less than $n$ which divide evenly into $n$).
If $d(a) = b$ and $d(b) = a$, where $a \ne b$, then $a$ and $b$ are an amicable pair and each of $a$ and $b$ are called amicable numbers.
For example, the proper divisors of $220$ are $1, 2, 4, 5, 10, 11, 20, 22, 44, 55$ and $110$; therefore $d(220) = 284$. The proper divisors of $284$ are $1, 2, 4, 71$ and $142$; so $d(284) = 220$.
Evaluate the sum of all the amicable numbers under $10000$.

友愛数¶

d(n) を n の真の約数の和と定義する. (真の約数とは n 以外の約数のことである. )
もし, d(a) = b かつ d(b) = a (a ≠ b のとき) を満たすとき, a と b は友愛数(親和数)であるという.

例えば, 220 の約数は 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110 なので d(220) = 284 である.
また, 284 の約数は 1, 2, 4, 71, 142 なので d(284) = 220 である.

それでは10000未満の友愛数の和を求めよ.