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As n ranges over the positive integers, what is the sum of all possible values of the greatest common divisor of 3n + 4 and n + 16?

 Dec 24, 2021
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n

1 GCD== 1
2 GCD== 2
3 GCD== 1
4 GCD== 4
5 GCD== 1
6 GCD== 22
7 GCD== 1
8 GCD== 4
9 GCD== 1
10 GCD== 2
11 GCD== 1
12 GCD== 4
13 GCD== 1
14 GCD== 2
15 GCD== 1
16 GCD== 4
17 GCD== 11
18 GCD== 2
19 GCD== 1
20 GCD== 4
21 GCD== 1
22 GCD== 2
23 GCD== 1
24 GCD== 4
25 GCD== 1
26 GCD== 2
27 GCD== 1
28 GCD== 44
SUM of all GCDs ==126

Note: if you wish to count only UNIQUE GCDs, then you have: 1, 2, 4, 11, 22, 44==84

 Dec 24, 2021

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