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Note that it is impossible to have three consecutive positive even integers which have odd sigma() values.
In order to have an odd sigma() value, the integer must be a square or twice a square; it's not too hard to see that three consecutive positive even integers can't each be a square or twice a square.
So any solution must have n odd, and among n+1 and n+3, one of them must be a square and the other must be twice a square.
Any other terms exceed 10^128.
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