2301
Factors of 1040 have the form 2m5n with 0 <= m, n <= 40. So there are 41² = 1681 such factors.
Factors of 2030 = 260530 not dividing 1040 have the form 2m5n with 41 <= m <= 60 and 0 <= n <= 30, so there are 20×31 = 620 such factors.
Altogether, there are 1681 + 620 = 2301 numbers matching the problem.
|