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Writing n as the product of k distinct positive integers
Problem 495
Published on 27 December 2014 at 10:00 pm [Server Time]
Let W(n,k) be the number of ways in which n can be written as the product of k distinct positive integers.
For example, W(144,4) = 7. There are 7 ways in which 144 can be written as a product of 4 distinct positive integers:
- 144 = 1×2×4×18
- 144 = 1×2×8×9
- 144 = 1×2×3×24
- 144 = 1×2×6×12
- 144 = 1×3×4×12
- 144 = 1×3×6×8
- 144 = 2×3×4×6
Note that permutations of the integers themselves are not considered distinct.
Furthermore, W(100!,10) modulo 1 000 000 007 = 287549200.
Find W(10000!,30) modulo 1 000 000 007.
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