Let $n$ be the least positive integer for which $149^n-2^n$ is divisible by $3^3\cdot5^5\cdot7^7.$ Find the number of positive integer divisors of n

Aniket Bhattacharyea Answered question

Lifting the Exponent shows that

so thus,

so thus,

Now, multiplying

and since

Since

Aniket Bhattacharyea Answered question