{"raw_statement":[{"iden":"statement","content":"Many great mathematicians have sequences named after them. Timmy is a great mathematician, so he created a sequence called $t$, but he needs help to compute its values. Let $t_i$ be the number of unordered triples $(a, b, c)$ where $a <= b <= c$ and $a dot.op b dot.op c = i$. For all $i$ from $1$ to $n$, find and print $t_i$.\n\nThe only line contains a single integer $n$ $(1 <= n <= 10^4)$.\n\nFor all $i$ from $1$ to $n$, print $t_i$.\n\nThere are $3$ triples that have product $8$: $(1, 1, 8)$, $(1, 2, 4)$, and $(2, 2, 2)$. However, there is only $1$ triple that has product $7$: $(1, 1, 7)$.\n\n"},{"iden":"input","content":"The only line contains a single integer $n$ $(1 <= n <= 10^4)$."},{"iden":"output","content":"For all $i$ from $1$ to $n$, print $t_i$."},{"iden":"note","content":"There are $3$ triples that have product $8$: $(1, 1, 8)$, $(1, 2, 4)$, and $(2, 2, 2)$. However, there is only $1$ triple that has product $7$: $(1, 1, 7)$."}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ n \\in \\mathbb{Z}^+ $ with $ 1 \\leq n \\leq 10^4 $.  \nFor each $ i \\in \\{1, 2, \\dots, n\\} $, define $ t_i $ as the number of unordered triples $ (a, b, c) \\in \\mathbb{Z}^+^3 $ such that $ a \\leq b \\leq c $ and $ a \\cdot b \\cdot c = i $.\n\n**Objective**  \nFor each $ i = 1 $ to $ n $, compute and output $ t_i $.","simple_statement":"Given n, for each i from 1 to n, count the number of unordered triples (a, b, c) with a ≤ b ≤ c such that a * b * c = i. Print each count on a new line.","has_page_source":false}