题目241:完美商
Perfection QuotientsFor a positive integer n, let σ(n) be the sum of all divisors of n, so e.g. σ(6) = 1 + 2 + 3 + 6 = 12.
A perfect number, as you probably know, is a number with σ(n) = 2n.
Let us define the perfection quotient of a positive integer as
Find the sum of all positive integers n ≤ 1018 for which p(n) has the form k + 1⁄2, where k is an integer.
题目:
对于一个正整数 n,设 σ(n) 为所有 n 的因数的和,于是有 σ(6) = 1 + 2 + 3 + 6 = 12。
你可能知道,完美数就是满足 σ(n) = 2n 的数。
定义一个正整数的完美商为
求所有满足以下条件的正整数 n 的和。
n ≤ 1018 且 p(n) = k + 1⁄2,其中 k 为整数。
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