ag-gipp/GoUldI

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data/178.json

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{
  "definitions" : {
    "n" : [ {
      "Q1667469" : "prime power",
      "Q28920044" : "positive integer"
    } ],
    "p" : [ {
      "Q49008" : "prime number"
    } ]
  },
  "constraints" : [ ],
  "math_inputtex" : "\\[\\Lambda\\left(n\\right)=\\ln p,\\]",
  "math_inputtex_semantic" : "\\wf{Q282327}{\\MangoldtLambda}@{\\w{Q1667469}{n}} = \\ln@@{\\w{Q49008}{p}}",
  "correct_tex" : "\\Lambda\\left(n\\right)=\\ln p",
  "correct_mml" : "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"p1.1.m1.1\" class=\"ltx_Math\" alttext=\"\\MangoldtLambda@{n}=\\ln@{p}\" display=\"inline\">\n  <semantics id=\"p1.1.m1.1a\">\n    <mrow id=\"p1.1.m1.1.4\" xref=\"p1.1.m1.1.4.cmml\">\n      <mrow id=\"p1.1.m1.1.1.8.2\" xref=\"p1.1.m1.1.1.1.cmml\">\n        <mpadded width=\"-1.7pt\" id=\"p1.1.m1.1.1.2\" xref=\"p1.1.m1.1.1.1.cmml\">\n          <mi mathvariant=\"normal\" id=\"p1.1.m1.1.1.2.1.2\" xref=\"p1.1.m1.1.1.2.1.1.cmml\">Λ</mi>\n        </mpadded>\n        <mo id=\"p1.1.m1.1.1.8.2a\" xref=\"p1.1.m1.1.1.1.cmml\">⁡</mo>\n        <mrow id=\"p1.1.m1.1.1.8.2.1\" xref=\"p1.1.m1.1.1.1.cmml\">\n          <mo id=\"p1.1.m1.1.1.5\" xref=\"p1.1.m1.1.1.1.cmml\">(</mo>\n          <mi id=\"p1.1.m1.1.1.6\" xref=\"p1.1.m1.1.1.6.cmml\">n</mi>\n          <mo id=\"p1.1.m1.1.1.7\" xref=\"p1.1.m1.1.1.1.cmml\">)</mo>\n        </mrow>\n      </mrow>\n      <mo id=\"p1.1.m1.1.2\" xref=\"p1.1.m1.1.2.cmml\">=</mo>\n      <mrow id=\"p1.1.m1.1.3.5\" xref=\"p1.1.m1.1.3.1.cmml\">\n        <mi id=\"p1.1.m1.1.3.2.1.2\" xref=\"p1.1.m1.1.3.2.1.1.cmml\">ln</mi>\n        <mo id=\"p1.1.m1.1.3.5a\" xref=\"p1.1.m1.1.3.1.cmml\">⁡</mo>\n        <mi id=\"p1.1.m1.1.3.4\" xref=\"p1.1.m1.1.3.4.cmml\">p</mi>\n      </mrow>\n    </mrow>\n    <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n      <apply id=\"p1.1.m1.1.4.cmml\" xref=\"p1.1.m1.1.4\">\n        <eq id=\"p1.1.m1.1.2.cmml\" xref=\"p1.1.m1.1.2\"/>\n        <apply id=\"p1.1.m1.1.1.1.cmml\" xref=\"p1.1.m1.1.1.8.2\">\n          <csymbol cd=\"dlmf\" id=\"p1.1.m1.1.1.2.1.1.cmml\" xref=\"p1.1.m1.1.1.2.1.2\">Mangoldt-Lambda</csymbol>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.1.6.cmml\" xref=\"p1.1.m1.1.1.6\">Q1667469</csymbol>\n        </apply>\n        <apply id=\"p1.1.m1.1.3.1.cmml\" xref=\"p1.1.m1.1.3.5\">\n          <ln id=\"p1.1.m1.1.3.2.1.1.cmml\" xref=\"p1.1.m1.1.3.2.1.2\"/>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.3.4.cmml\" xref=\"p1.1.m1.1.3.4\">Q49008</csymbol>\n        </apply>\n      </apply>\n    </annotation-xml>\n    <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">\\MangoldtLambda@{n}=\\ln@{p}</annotation>\n  </semantics>\n</math>",
  "uri" : "http://dlmf.nist.gov/27.2#E14",
  "title" : "DLMF:_27.2_Functions",
  "type" : "definition"
}