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

231 sonini tub ko‘paytuvchisiga ajrating: $231 = 3 \times 7 \times 11$. Har bir tub omilni bir martta yoki nol martta qo‘shib, bo‘luvchilarni olish uchun formuladan foydalanamiz: agar $n = p_1^{a_1}p_2^{a_2}\dots p_k^{a_k}$ bo‘lsa, bo‘luvchilar soni $\displaystyle\prod_{i=1}^{k}(a_i+1)$, bo‘luvchilar yig‘indisi esa $\displaystyle\prod_{i=1}^{k}\frac{p_i^{a_i+1}-1}{p_i-1}$. Bu holda $a_1=a_2=a_3=1$, shuning uchun bo‘luvchilar yig‘indisi \[ \left(\frac{3^{2}-1}{3-1}\right)\!\!\times\!\left(\frac{7^{2}-1}{7-1}\right)\!\!\times\!\left(\frac{11^{2}-1}{11-1}\right) = \frac{9-1}{2}\times\frac{49-1}{6}\times\frac{121-1}{10} =4\times8\times12=384. \] Demak, 231 sonining natural bo‘luvchilari yig‘indisi $384$ ga teng, ya’ni javob **B**.