data/36.json
{
"definitions": {
"n": [
{
"Q21199": "natural number (numbers used for counting and ordering)"
}
],
"i": [
{
"Q2303886": "index (the numbering of various objects within the mathematical notation)"
}
],
"r": [
{
"Q2303886": "index (the numbering of various objects within the mathematical notation)"
}
],
"p_{i}": [
{
"Q1137759": " prime factor ( prime number dividing an integer )"
}
],
"a_{i}": [
"maximum power",
{}
]
},
"constraints": [],
"math_inputtex": "n = \\prod_{i=1}^r p_i^{a_i}",
"math_inputtex_semantic": "\\w{Q21199}{n} = \\prod_{\\w{Q2303886}{i}=1}^{\\w{Q2303886}{r}} \\w{Q1137759}{p}_i^{\\w{Q10578722}{a}_i}",
"correct_tex": "n = \\prod_{i=1}^r p_i^{a_i}",
"correct_mml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"\n xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n alttext=\"n=\\prod_{i=1}^{r}p_{i}^{a_{i}}\"\n class=\"ltx_Math\"\n display=\"inline\"\n id=\"p1.1.m1.1\">\n <semantics id=\"p1.1.m1.1a\">\n <mrow id=\"p1.1.m1.1.9\" xref=\"p1.1.m1.1.9.cmml\">\n <mi id=\"p1.1.m1.1.1\" xref=\"p1.1.m1.1.1.cmml\">n</mi>\n <mo id=\"p1.1.m1.1.2\" xref=\"p1.1.m1.1.2.cmml\">=</mo>\n <mrow id=\"p1.1.m1.1.9.1\" xref=\"p1.1.m1.1.9.1.cmml\">\n <msubsup id=\"p1.1.m1.1.9.1.1\" xref=\"p1.1.m1.1.9.1.1.cmml\">\n <mo id=\"p1.1.m1.1.3\"\n largeop=\"true\"\n symmetric=\"true\"\n xref=\"p1.1.m1.1.3.cmml\">∏</mo>\n <mrow id=\"p1.1.m1.1.4.1\" xref=\"p1.1.m1.1.4.1.cmml\">\n <mi id=\"p1.1.m1.1.4.1.1\" xref=\"p1.1.m1.1.4.1.1.cmml\">i</mi>\n <mo id=\"p1.1.m1.1.4.1.2\" xref=\"p1.1.m1.1.4.1.2.cmml\">=</mo>\n <mn id=\"p1.1.m1.1.4.1.3\" xref=\"p1.1.m1.1.4.1.3.cmml\">1</mn>\n </mrow>\n <mi id=\"p1.1.m1.1.5.1\" xref=\"p1.1.m1.1.5.1.cmml\">r</mi>\n </msubsup>\n <msubsup id=\"p1.1.m1.1.9.1.2\" xref=\"p1.1.m1.1.9.1.2.cmml\">\n <mi id=\"p1.1.m1.1.6\" xref=\"p1.1.m1.1.6.cmml\">p</mi>\n <mi id=\"p1.1.m1.1.7.1\" xref=\"p1.1.m1.1.7.1.cmml\">i</mi>\n <msub id=\"p1.1.m1.1.8.1\" xref=\"p1.1.m1.1.8.1.cmml\">\n <mi id=\"p1.1.m1.1.8.1.1\" xref=\"p1.1.m1.1.8.1.1.cmml\">a</mi>\n <mi id=\"p1.1.m1.1.8.1.2.1\" xref=\"p1.1.m1.1.8.1.2.1.cmml\">i</mi>\n </msub>\n </msubsup>\n </mrow>\n </mrow>\n <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n <apply id=\"p1.1.m1.1.9.cmml\" xref=\"p1.1.m1.1.9\">\n <eq id=\"p1.1.m1.1.2.cmml\" xref=\"p1.1.m1.1.2\"/>\n <ci id=\"p1.1.m1.1.1.cmml\" xref=\"p1.1.m1.1.1\">𝑛</ci>\n <apply id=\"p1.1.m1.1.9.1.cmml\" xref=\"p1.1.m1.1.9.1\">\n <apply id=\"p1.1.m1.1.9.1.1.cmml\" xref=\"p1.1.m1.1.9.1.1\">\n <power id=\"p1.1.m1.1.9.1.1.1.cmml\" xref=\"p1.1.m1.1.9.1.1\"/>\n <apply id=\"p1.1.m1.1.9.1.1.2.cmml\" xref=\"p1.1.m1.1.9.1.1\">\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.3.cmml\" xref=\"p1.1.m1.1.3\">product</csymbol>\n <apply id=\"p1.1.m1.1.4.1.cmml\" xref=\"p1.1.m1.1.4.1\">\n <eq id=\"p1.1.m1.1.4.1.2.cmml\" xref=\"p1.1.m1.1.4.1.2\"/>\n <ci id=\"p1.1.m1.1.4.1.1.cmml\" xref=\"p1.1.m1.1.4.1.1\">𝑖</ci>\n <cn id=\"p1.1.m1.1.4.1.3.cmml\" type=\"integer\" xref=\"p1.1.m1.1.4.1.3\">1</cn>\n </apply>\n </apply>\n <ci id=\"p1.1.m1.1.5.1.cmml\" xref=\"p1.1.m1.1.5.1\">𝑟</ci>\n </apply>\n <apply id=\"p1.1.m1.1.9.1.2.cmml\" xref=\"p1.1.m1.1.9.1.2\">\n <power id=\"p1.1.m1.1.9.1.2.1.cmml\" xref=\"p1.1.m1.1.9.1.2\"/>\n <apply id=\"p1.1.m1.1.9.1.2.2.cmml\" xref=\"p1.1.m1.1.9.1.2\">\n <ci id=\"p1.1.m1.1.6.cmml\" xref=\"p1.1.m1.1.6\">𝑝</ci>\n <ci id=\"p1.1.m1.1.7.1.cmml\" xref=\"p1.1.m1.1.7.1\">𝑖</ci>\n </apply>\n <apply id=\"p1.1.m1.1.8.1.cmml\" xref=\"p1.1.m1.1.8.1\">\n <ci id=\"p1.1.m1.1.8.1.1.cmml\" xref=\"p1.1.m1.1.8.1.1\">𝑎</ci>\n <ci id=\"p1.1.m1.1.8.1.2.1.cmml\" xref=\"p1.1.m1.1.8.1.2.1\">𝑖</ci>\n </apply>\n </apply>\n </apply>\n </apply>\n </annotation-xml>\n <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">n=\\prod_{i=1}^{r}p_{i}^{a_{i}}</annotation>\n </semantics>\n</math>\n",
"uri": "https://en.formulasearchengine.com/w/index.php?oldid=4630#math4630.12",
"title": "Divisor_function",
"type": "equation",
"check": {
"tree": false,
"qid": false
}
}