"Möbius function" meaning in All languages combined

{
  "etymology_text": "Named after August Ferdinand Möbius (1790–1868), a German mathematician and theoretical astronomer who introduced it in 1832.",
  "head_templates": [
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      "expansion": "Möbius function (uncountable)",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Combinatorics",
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        {
          "kind": "topical",
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          "name": "Functions",
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            "Formal sciences",
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            "Fundamental"
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          "source": "w"
        }
      ],
      "glosses": [
        "A function from the natural numbers to the set {−1, 0, 1} which maps perfect squares to 0, prime numbers to −1, and is multiplicative."
      ],
      "id": "en-Möbius_function-en-noun-bmf8F9MF",
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          "combinatorics",
          "combinatorics"
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        [
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        [
          "square",
          "square"
        ],
        [
          "prime number",
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        [
          "multiplicative",
          "multiplicative"
        ]
      ],
      "raw_glosses": [
        "(combinatorics) A function from the natural numbers to the set {−1, 0, 1} which maps perfect squares to 0, prime numbers to −1, and is multiplicative."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "combinatorics",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "August Ferdinand Möbius",
        "Möbius function"
      ]
    }
  ],
  "word": "Möbius function"
}

{
  "etymology_text": "Named after August Ferdinand Möbius (1790–1868), a German mathematician and theoretical astronomer who introduced it in 1832.",
  "head_templates": [
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      "expansion": "Möbius function (uncountable)",
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  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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        "English lemmas",
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        "English nouns",
        "English terms spelled with Ö",
        "English terms spelled with ◌̈",
        "English uncountable nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Combinatorics",
        "en:Functions"
      ],
      "glosses": [
        "A function from the natural numbers to the set {−1, 0, 1} which maps perfect squares to 0, prime numbers to −1, and is multiplicative."
      ],
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        [
          "combinatorics",
          "combinatorics"
        ],
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          "natural number",
          "natural number"
        ],
        [
          "square",
          "square"
        ],
        [
          "prime number",
          "prime number"
        ],
        [
          "multiplicative",
          "multiplicative"
        ]
      ],
      "raw_glosses": [
        "(combinatorics) A function from the natural numbers to the set {−1, 0, 1} which maps perfect squares to 0, prime numbers to −1, and is multiplicative."
      ],
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        "uncountable"
      ],
      "topics": [
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        "mathematics",
        "sciences"
      ],
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        "Möbius function"
      ]
    }
  ],
  "word": "Möbius function"
}