Problem 272

Modular Cubes, part 2

For a positive number `n`, define C(`n`) as the number of the integers `x,` for which 1`x``n` and`x`^{3}1 mod `n`.

When `n`=91, there are 8 possible values for `x`, namely : 9, 16, 22, 29, 53, 74, 79, 81.

Thus, C(91)=8.

Find the sum of the positive numbers `n`10^{11} for which C(`n`)=242.

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