{"problem":{"name":"C. Constant Ratio","description":{"content":"Given an integer n, find out number of ways to represent it as the sum of two or more integers ai with the next property: ratio ai / ai - 1 is the same positive integer for all possible i > 1. Input ","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":1000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10091C"},"statements":[{"statement_type":"Markdown","content":"Given an integer n, find out number of ways to represent it as the sum of two or more integers ai with the next property: ratio ai / ai - 1 is the same positive integer for all possible i > 1.\n\nInput consists of one integer n (1 ≤ n ≤ 105).\n\nPrint one integer — number of representations.\n\nIn the first sample no such representation exists.\n\nIn the second sample there exist two representations:\n\n## Input\n\nInput consists of one integer n (1 ≤ n ≤ 105).\n\n## Output\n\nPrint one integer — number of representations.\n\n[samples]\n\n## Note\n\nIn the first sample no such representation exists.In the second sample there exist two representations:  1 1 1 1 1, then q = 1.  1 4, then q = 4.","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ n \\in \\mathbb{Z} $ with $ 1 \\leq n \\leq 10^5 $.  \nA representation of $ n $ is a sequence of integers $ (a_1, a_2, \\dots, a_k) $ with $ k \\geq 2 $, such that:  \n- $ \\sum_{i=1}^k a_i = n $,  \n- $ a_i \\in \\mathbb{Z}^+ $ for all $ i $,  \n- $ \\frac{a_i}{a_{i-1}} = r $ for all $ i \\in \\{2, \\dots, k\\} $, where $ r \\in \\mathbb{Z}^+ $ is a constant ratio.\n\n**Objective**  \nCount the number of such sequences $ (a_1, a_2, \\dots, a_k) $ satisfying the above conditions.","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10091C","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}