+ <li>The perfect numbers between <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn><mjx-mstyle><mjx-mspace style="width: 0.167em;"></mjx-mspace></mjx-mstyle><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mstyle scriptlevel="0"><mspace width="0.167em"></mspace></mstyle><mn>000</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$1\,000$</span></mjx-container> and <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c39"></mjx-c></mjx-mn><mjx-mstyle><mjx-mspace style="width: 0.167em;"></mjx-mspace></mjx-mstyle><mjx-mn class="mjx-n"><mjx-c class="mjx-c39"></mjx-c><mjx-c class="mjx-c39"></mjx-c><mjx-c class="mjx-c39"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mstyle scriptlevel="0"><mspace width="0.167em"></mspace></mstyle><mn>999</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$9\,999$</span></mjx-container> inclusive. A perfect number is a positive integer which is equal to the sum of its proper divisors. A proper divisor is any divisor less than the number itself. For example, <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c36"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$6$</span></mjx-container> is a perfect number since <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="3"><mjx-c class="mjx-c2B"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="3"><mjx-c class="mjx-c32"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="3"><mjx-c class="mjx-c2B"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="3"><mjx-c class="mjx-c33"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c36"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>=</mo><mn>6</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$1 + 2 + 3 = 6$</span></mjx-container>.</li>
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