Sum of GCD's?!

Algebra Level 4

Consider the sequence 50+n2 50 + n^2 for positive integer nn:

51,54,59,66,75,51, 54, 59, 66, 75, \ldots

If we take the greatest common divisor of 2 consecutive terms, we obtain

3,1,1,3,3, 1, 1, 3, \ldots

What is the sum of all distinct elements in the second series?

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