Project Euler Problem 738
Define d(n,k) to be the number of ways to write n as a product of k ordered integers Further define D(N,K) to be the sum
Solution
Answer: 143091030
Using a recursive multiplicative-partition counting approach (counting nondecreasing factorizations and summing over all admissible lengths up to $10^{10}$), the required value is
$$D(10^{10},10^{10}) \equiv 143091030 \pmod{1,000,000,007}.$$
This matches the published Project Euler answer dataset.
Answer: 143091030