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Problem 840

AMC 12 late, AIME early

Number theory Difficulty 4.6 Find the answer HMMT November

Find the number of positive integers less than 1000000 which are less than or equal to the sum of their proper divisors. If your answer is $X$ and the actual value is $Y$ , your score will be $\max \left(0,20-80\left|1-\frac{X}{Y}\right|\right)$ rounded to the nearest integer.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

$\mathrm{N}=1000000$ $\mathrm{s}=[0] * \mathrm{~N}$ ans $=0$ for i in range(1, N): if i <= s*: ans $+=1$ for $j$ in range(i + i, N, i): $s[j]+=$ i print(ans)

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.