9900=2^2*3^2*5^2*11, 4 prime factors (A=2, B=3, C=5, D=11) combined as a product: AABBCCD. When split into 26 pairs of factors we have:
1:(A,ABBCCD), 2:(B,AABCD), 3:(C,AABBCD), 4:(D,AABBCC), 5:(AA,BBCCD), 6:(AB,ABCCD), 7:(AC,ABBCD), 8:(AD,ABBCC), 9:(BB,AACCD), 10:(BC,AABCD), 11:(BD,AABCC), 12:(CC,AABBD), 13:(CD,AABBC), 14:(AAB,BCCD), 15:(AAC,BBCD), 16:(AAD,BBCC), 17:(ABB,ACCD), 18:(ABC,ABCD), 19:(ABD,ABCC), 20:(ACC,ABBD), 21:(ACD,ABBC), 22:(BBC,AACD), 23:(BBD,AACC), 24:(BCC,AABD), 25:(BCD,AABC), 26:(CCD,AABB).
Progressively, we can work out all the actual numerical divisors by pair grouping in numerical order of the first divisor:
1:(2,4950), 2:(3,3300), 5:(4,2475), 3:(5,1980), 6:(6,1650), 9:(9,1100), 7:(10,990), 4:(11,900), 14:(12,825), 10:(15,660), 17:(18,550), 15:(20,495), 8:(22,450), 12:(25,396), 18:(30,330), 11:(33,300), 26:(36,275), 16:(44,225), 22:(45,220), 20:(50,198), 13:(55,180), 25:(60,165), 19:(66,150), 24:(75,132), 21:(90,110), 23:(99,100).
There are 26 pairs, matching expectation according to the index (number followed by a colon in front of the pair). Note that the order of divisors in the pair is not important when matching. Hence we know that no pairs are missing and no factor is duplicated.
The sum of each pair is: 4952, 3303, 2479, 1985, 1656, 1109, 1000, 911, 837, 675, 568, 515, 472, 421, 360, 333, 311, 269, 265, 248, 235, 225, 216, 207, 200, 199.
TOTAL: 23951.
If 1 and 9900 are also added, we have 33852.