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

144 sonini tub ko‘paytuvchilarga ajratamiz: $144 = 2^{4}\cdot 3^{2}$. Agar $n = p_{1}^{a_{1}}p_{2}^{a_{2}}\dots p_{k}^{a_{k}}$ bo‘lsa, uning barcha natural bo‘luvchilarining yig‘indisi \[ \sigma (n)=\prod_{i=1}^{k}\frac{p_{i}^{a_{i}+1}-1}{p_{i}-1} \] formula bilan hisoblanadi. Shu holda \[ \sigma(144)=\frac{2^{4+1}-1}{2-1}\cdot\frac{3^{2+1}-1}{3-1} =\frac{32-1}{1}\cdot\frac{27-1}{2} =31\cdot13=403. \] Demak, 144 sonining natural bo‘luvchilar yig‘indisi **403** ga teng, ya’ni javob **D**.