15:{"metadata":[["$","title","0",{"children":"A New Classification of Positive Integers Via New Divisor Functions"}],["$","meta","1",{"name":"description","content":"Let $d_1 = 1 < d_2 < d_3 < \\cdots < d_{\\tau(n)} = n$ denote the increasing sequence of the divisors of a positive integer $n$. In this paper, for real or complex values of $\\alpha$, we define and study some properties of two new divisor functions $\\sigma_{e,\\alpha}$ and $\\sigma_{o,\\alpha}$. The first computes the sum of the $\\alpha$-th powers of the divisors of $n$ with even indices, and the second computes the sum of the $\\alpha$-th powers of the divisors of $n$ with odd indices. We also introduce a new type of positive integers, namely, $k$-index ratio numbers and state three conjectures related to them."}],["$","meta","2",{"name":"author","content":"Brahim Mittou"}],["$","meta","3",{"name":"keywords","content":"General Mathematics"}],["$","meta","4",{"name":"referrer","content":"origin"}],["$","meta","5",{"name":"robots","content":"index, follow"}],["$","link","6",{"rel":"canonical","href":"https://synthical.com/article/A-New-Classification-of-Positive-Integers-Via-New-Divisor-Functions-a4201b27-27c3-40fb-8953-abbe5498a4ce"}],["$","link","7",{"rel":"alternate","hrefLang":"de-DE","href":"https://synthical.com/article/A-New-Classification-of-Positive-Integers-Via-New-Divisor-Functions-a4201b27-27c3-40fb-8953-abbe5498a4ce/de"}],["$","link","8",{"rel":"alternate","hrefLang":"fr-FR","href":"https://synthical.com/article/A-New-Classification-of-Positive-Integers-Via-New-Divisor-Functions-a4201b27-27c3-40fb-8953-abbe5498a4ce/fr"}],["$","link","9",{"rel":"alternate","hrefLang":"es-ES","href":"https://synthical.com/article/A-New-Classification-of-Positive-Integers-Via-New-Divisor-Functions-a4201b27-27c3-40fb-8953-abbe5498a4ce/es"}],["$","link","10",{"rel":"alternate","hrefLang":"it-IT","href":"https://synthical.com/article/A-New-Classification-of-Positive-Integers-Via-New-Divisor-Functions-a4201b27-27c3-40fb-8953-abbe5498a4ce/it"}],["$","link","11",{"rel":"alternate","hrefLang":"ru-RU","href":"https://synthical.com/article/A-New-Classification-of-Positive-Integers-Via-New-Divisor-Functions-a4201b27-27c3-40fb-8953-abbe5498a4ce/ru"}],["$","meta","12",{"property":"og:title","content":"A New Classification of Positive Integers Via New Divisor Functions"}],["$","meta","13",{"property":"og:description","content":"Let $d_1 = 1 < d_2 < d_3 < \\cdots < d_{\\tau(n)} = n$ denote the increasing sequence of the divisors of a positive integer $n$. 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We also introduce a new type of positive integers, namely, $k$-index ratio numbers and state three conjectures related to them."}],["$","meta","14",{"property":"og:url","content":"https://synthical.com/article/A-New-Classification-of-Positive-Integers-Via-New-Divisor-Functions-a4201b27-27c3-40fb-8953-abbe5498a4ce"}],["$","meta","15",{"property":"og:site_name","content":"Synthical"}],["$","meta","16",{"property":"og:locale","content":"en-US"}],["$","meta","17",{"property":"og:image","content":"https://synthical.com/preview/article/a4201b27-27c3-40fb-8953-abbe5498a4ce"}],["$","meta","18",{"property":"og:image:alt","content":"A New Classification of Positive Integers Via New Divisor Functions"}],["$","meta","19",{"property":"og:image:width","content":"1200"}],["$","meta","20",{"property":"og:image:height","content":"630"}],["$","meta","21",{"property":"og:type","content":"article"}],["$","meta","22",{"property":"article:published_time","content":"2025-09-07T06:14:16.000Z"}],["$","meta","23",{"property":"article:modified_time","content":"2025-09-14T21:01:16.000Z"}],["$","meta","24",{"property":"article:author:name","content":"Brahim Mittou"}],["$","meta","25",{"property":"article:author:id","content":"db2e7baa-17df-4f99-9a23-e2a0c56f5819"}],["$","meta","26",{"property":"article:author:alternatives","content":"Brahim Mittou,B. 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