σ(a) = σ(b) = a + b – 1

$\sigma(a) \; = \; \sigma(b) \; = \; a \; + \; b \; - \; 1$

For example,

$\sigma(6160) \; = \; \sigma(11697) \; = \; 17856 \; = \; 6160 \; + \; 11697 \; - \; 1$

$\sigma(12220) \; = \; \sigma(16005) \; = \; 28224 \; = \; 12220 \; + \; 16005 \; - \; 1$

$\sigma(23500) \; = \; \sigma(28917) \; = \; 52416 \; = \; 23500 \; + \; 28917 \; - \; 1$

$\sigma(68908) \; = \; \sigma(76245) \; = \; 145152 \; = \; 68908 \; + \; 76245 \; - \; 1$

$\sigma(249424) \; = \; \sigma(339825) \; = \; 589248 \; = \; 249424 \; + \; 339825 \; - \; 1$

$\sigma(425500) \; = \; \sigma(570405) \; = \; 995904 \; = \; 425500 \; + \; 570405 \; - \; 1$

$\sigma(434784) \; = \; \sigma(871585) \; = \; 1306368 \; = \; 434784 \; + \; 871585 \; - \; 1$

$\sigma(649990) \; = \; \sigma(697851) \; = \; 1347840 \; = \; 649990 \; + \; 697851 \; - \; 1$

$\sigma(660825) \; = \; \sigma(678376) \; = \; 1339200 \; = \; 660825 \; + \; 678376 \; - \; 1$

$\sigma(1017856) \; = \; \sigma(1340865) \; = \; 2358720 \; = \; 1017856 \; + \; 1340865 \; - \; 1$

$\sigma(1077336) \; = \; \sigma(2067625) \; = \; 3144960 \; = \; 1077336 \; + \; 2067625 \; - \; 1$

Can you find other solutions?