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

48 sonining natural bo‘luvchilarini topamiz. 48 ni tub omillarga ajratamiz: $48 = 2^{4}\cdot 3^{1}$. Naturlik bo‘luvchilar soni formulasi $ (a+1)(b+1)\dots $ bo‘lib, bu yerda $a,b$ – tegishli tub omillarning darajalari. Shuning uchun bo‘luvchilar soni $ (4+1)(1+1)=5\cdot 2=10$. Bo‘luvchilar yig‘indisi formulasi $\displaystyle \sigma (n)=\prod_{i}\frac{p_i^{k_i+1}-1}{p_i-1}$. Shu holda \[ \sigma(48)=\frac{2^{4+1}-1}{2-1}\cdot\frac{3^{1+1}-1}{3-1} = \frac{2^{5}-1}{1}\cdot\frac{3^{2}-1}{2} = (32-1)\cdot\frac{9-1}{2} = 31\cdot4=124 . \] Demak, 48 sonining natural bo‘luvchilar yig‘indisi **124**, ya’ni javob **C**.