Bo'linuvchanlik. Sonning natural bo'luvchilar soni va yig'indisi bo‘yicha savol

550 sonini tub ko‘paytuvchilarga ajratamiz: $550 = 2 \cdot 5^{2} \cdot 11$. Agar $n = p_{1}^{a_{1}}p_{2}^{a_{2}}\dots p_{k}^{a_{k}}$ bo‘lsa, uning bo‘luvchilar yig‘indisi formulasi $ \sigma(n)=\prod_{i=1}^{k}\frac{p_{i}^{a_{i}+1}-1}{p_{i}-1}$ bo‘ladi. Shunday qilib, \[ \sigma(550)=\frac{2^{1+1}-1}{2-1}\cdot\frac{5^{2+1}-1}{5-1}\cdot\frac{11^{1+1}-1}{11-1} = (2^{2}-1)\cdot\frac{5^{3}-1}{4}\cdot\frac{11^{2}-1}{10}. \] Hisoblaymiz: $2^{2}-1=3$, $5^{3}=125$ dan $\frac{125-1}{4}=31$, $11^{2}=121$ dan $\frac{121-1}{10}=12$. Endi $3\cdot31\cdot12=1116$. Demak, 550 sonining natural bo‘luvchilar yig‘indisi **1116**, ya’ni variant **D**.