Wolstenholme numbers
J, 39 35 30 28 bytes
(]{~1+i.~)1*.[:+/\_2^~1+i.,]

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-5 thanks to Bubbler's observation that the numerator is the LCM of the fraction and 1.
-2 thanks to Bubbler for a transformation.
Note: The approach below relies on the assumption that every Wolstenholme number is greater than or equal its index, which was kindly proved by Greg Martin.

[:+/\_2^~1+i.,] Generates the sequence up to n+1, where n is the input: Scan sum +/\ of 1 over 1% the square of *: one plus 1...+ the integers from 0 to the input i.@&gt;:.
1*. Numerators only.
(]{~1+i.~) Finds index of the input in previous result, adds 1, and plucks from previous result.