--description--

Consider the number 15.

There are eight positive numbers less than 15 which are coprime to 15: 1, 2, 4, 7, 8, 11, 13, 14.

The modular inverses of these numbers modulo 15 are: 1, 8, 4, 13, 2, 11, 7, 14 because

$$\begin{align} & 1 \times 1\bmod 15 = 1 \\ & 2 \times 8 = 16\bmod 15 = 1 \\ & 4 \times 4 = 16\bmod 15 = 1 \\ & 7 \times 13 = 91\bmod 15 = 1 \\ & 11 \times 11 = 121\bmod 15 = 1 \\ & 14 \times 14 = 196\bmod 15 = 1 \end{align}$$

Let $I(n)$ be the largest positive number $m$ smaller than $n - 1$ such that the modular inverse of $m$ modulo $n$ equals $m$ itself.

So $I(15) = 11$.

Also $I(100) = 51$ and $I(7) = 1$.

Find $\sum I(n)$ for $3 ≤ n ≤ 2 \times {10}^7$

--hints--

modularInverses() should return 153651073760956.

assert.strictEqual(modularInverses(), 153651073760956);

--seed--

--seed-contents--

function modularInverses() {

  return true;
}

modularInverses();

--solutions--

// solution required