Integer Factorization with Specific Pattern
Clash Royale CLAN TAG#URR8PPP
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Given a pattern vector $vecv=(e_1,cdots,e_k)$ whose elements are positive integers (not necessarily distinct), I'd like to ask how many ways to write $N!$ as $prod_i=1^k b_i^e_i$ where $b_1 cdots b_k$ are distinct positive integers. Note that permutations of $b_i$ do not count as different ways. For example, given $vecv=(1,1)$ and $N=3$, there are two ways: $3!=1 times6$ and $3!=2 times 3$.
combinatorics integers prime-factorization
asked Sep 9 at 13:03
Hang Wu
14410
add a comment |Â
up vote
-1
down vote
favorite
Given a pattern vector $vecv=(e_1,cdots,e_k)$ whose elements are positive integers (not necessarily distinct), I'd like to ask how many ways to write $N!$ as $prod_i=1^k b_i^e_i$ where $b_1 cdots b_k$ are distinct positive integers. Note that permutations of $b_i$ do not count as different ways. For example, given $vecv=(1,1)$ and $N=3$, there are two ways: $3!=1 times6$ and $3!=2 times 3$.
combinatorics integers prime-factorization
asked Sep 9 at 13:03
Hang Wu
14410
1
Project Euler 636?
– rogerl
Sep 9 at 13:33
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Given a pattern vector $vecv=(e_1,cdots,e_k)$ whose elements are positive integers (not necessarily distinct), I'd like to ask how many ways to write $N!$ as $prod_i=1^k b_i^e_i$ where $b_1 cdots b_k$ are distinct positive integers. Note that permutations of $b_i$ do not count as different ways. For example, given $vecv=(1,1)$ and $N=3$, there are two ways: $3!=1 times6$ and $3!=2 times 3$.
combinatorics integers prime-factorization
asked Sep 9 at 13:03
Hang Wu
14410
Given a pattern vector $vecv=(e_1,cdots,e_k)$ whose elements are positive integers (not necessarily distinct), I'd like to ask how many ways to write $N!$ as $prod_i=1^k b_i^e_i$ where $b_1 cdots b_k$ are distinct positive integers. Note that permutations of $b_i$ do not count as different ways. For example, given $vecv=(1,1)$ and $N=3$, there are two ways: $3!=1 times6$ and $3!=2 times 3$.
combinatorics integers prime-factorization
combinatorics integers prime-factorization
asked Sep 9 at 13:03
Hang Wu
14410
asked Sep 9 at 13:03
Hang Wu
14410
asked Sep 9 at 13:03
Hang Wu
14410
asked Sep 9 at 13:03
Hang Wu
14410
asked Sep 9 at 13:03
Hang Wu
14410
14410
1
Project Euler 636?
– rogerl
Sep 9 at 13:33
add a comment |Â
1
Project Euler 636?
– rogerl
Sep 9 at 13:33
1
1
Project Euler 636?
– rogerl
Sep 9 at 13:33
Project Euler 636?
– rogerl
Sep 9 at 13:33
add a comment |Â
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1
Project Euler 636?
– rogerl
Sep 9 at 13:33