"superabundant number" meaning in English

{
  "forms": [
    {
      "form": "superabundant numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "superabundant number (plural superabundant numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Number theory",
          "orig": "en:Number theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "86 14",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        }
      ],
      "examples": [
        {
          "text": "1984, Richard K. Guy (editor), Reviews in Number Theory 1973-83, Volume 4, Part 1, As printed in Mathematical Reviews, American Mathematical Society, page 173,\nThe authors prove a theorem: If Q(X) is the number of superabundant numbers ≦X, then for c<5/48,Q(X)≧( log X)¹⁺ᶜ for sufficiently large X."
        },
        {
          "text": "1995, József Sándor, Dragoslav S. Mitrinović, Borislav Crstici, Handbook of Number Theory I, Springer, page 111,\n1) A number n is called superabundant if (σ(n))/n>(σ(m))/m for all m with 1Corollary. Q(x)>c log x log log x/( log log log x)²."
        },
        {
          "ref": "2017, Kevin Broughan, Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents, Cambridge University Press, page 151",
          "text": "It follows that there is a superabundant number in each real interval #x5B;x,2x#x5D; and that the number of superabundant numbers is thus infinite.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A positive integer whose abundancy index is greater than that of any lesser positive integer."
      ],
      "id": "en-superabundant_number-en-noun-fR0OwRPs",
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "positive",
          "positive"
        ],
        [
          "integer",
          "integer"
        ],
        [
          "abundancy index",
          "abundancy index"
        ]
      ],
      "raw_glosses": [
        "(number theory) A positive integer whose abundancy index is greater than that of any lesser positive integer."
      ],
      "synonyms": [
        {
          "_dis1": "97 3",
          "sense": "positive integer whose abundancy index is greater than that of any lesser positive integer",
          "tags": [
            "abbreviation"
          ],
          "word": "SA"
        },
        {
          "_dis1": "97 3",
          "alt": "Ramanujan",
          "sense": "positive integer whose abundancy index is greater than that of any lesser positive integer",
          "word": "superior highly composite number"
        }
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "translations": [
        {
          "_dis1": "97 3",
          "code": "fi",
          "lang": "Finnish",
          "sense": "positive integer whose abundancy index is greater than that of any lesser positive integer",
          "word": "ylirunsas luku"
        },
        {
          "_dis1": "97 3",
          "code": "fr",
          "lang": "French",
          "sense": "positive integer whose abundancy index is greater than that of any lesser positive integer",
          "tags": [
            "masculine"
          ],
          "word": "nombre superabondant"
        }
      ]
    },
    {
      "glosses": [
        "Used other than figuratively or idiomatically: see superabundant, number."
      ],
      "id": "en-superabundant_number-en-noun-FaeWhtwO",
      "links": [
        [
          "superabundant",
          "superabundant#English"
        ],
        [
          "number",
          "number#English"
        ]
      ],
      "related": [
        {
          "_dis1": "30 70",
          "word": "abundant number"
        },
        {
          "_dis1": "30 70",
          "word": "highly abundant number"
        },
        {
          "_dis1": "30 70",
          "word": "superabundant"
        }
      ]
    }
  ],
  "wikipedia": [
    "superabundant number"
  ],
  "word": "superabundant number"
}

{
  "categories": [
    "English countable nouns",
    "English entries with incorrect language header",
    "English lemmas",
    "English multiword terms",
    "English nouns"
  ],
  "forms": [
    {
      "form": "superabundant numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "superabundant number (plural superabundant numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "abundant number"
    },
    {
      "word": "highly abundant number"
    },
    {
      "word": "superabundant"
    }
  ],
  "senses": [
    {
      "categories": [
        "English terms with quotations",
        "en:Number theory"
      ],
      "examples": [
        {
          "text": "1984, Richard K. Guy (editor), Reviews in Number Theory 1973-83, Volume 4, Part 1, As printed in Mathematical Reviews, American Mathematical Society, page 173,\nThe authors prove a theorem: If Q(X) is the number of superabundant numbers ≦X, then for c<5/48,Q(X)≧( log X)¹⁺ᶜ for sufficiently large X."
        },
        {
          "text": "1995, József Sándor, Dragoslav S. Mitrinović, Borislav Crstici, Handbook of Number Theory I, Springer, page 111,\n1) A number n is called superabundant if (σ(n))/n>(σ(m))/m for all m with 1Corollary. Q(x)>c log x log log x/( log log log x)²."
        },
        {
          "ref": "2017, Kevin Broughan, Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents, Cambridge University Press, page 151",
          "text": "It follows that there is a superabundant number in each real interval #x5B;x,2x#x5D; and that the number of superabundant numbers is thus infinite.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A positive integer whose abundancy index is greater than that of any lesser positive integer."
      ],
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "positive",
          "positive"
        ],
        [
          "integer",
          "integer"
        ],
        [
          "abundancy index",
          "abundancy index"
        ]
      ],
      "raw_glosses": [
        "(number theory) A positive integer whose abundancy index is greater than that of any lesser positive integer."
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ]
    },
    {
      "glosses": [
        "Used other than figuratively or idiomatically: see superabundant, number."
      ],
      "links": [
        [
          "superabundant",
          "superabundant#English"
        ],
        [
          "number",
          "number#English"
        ]
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "positive integer whose abundancy index is greater than that of any lesser positive integer",
      "tags": [
        "abbreviation"
      ],
      "word": "SA"
    },
    {
      "alt": "Ramanujan",
      "sense": "positive integer whose abundancy index is greater than that of any lesser positive integer",
      "word": "superior highly composite number"
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "positive integer whose abundancy index is greater than that of any lesser positive integer",
      "word": "ylirunsas luku"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "positive integer whose abundancy index is greater than that of any lesser positive integer",
      "tags": [
        "masculine"
      ],
      "word": "nombre superabondant"
    }
  ],
  "wikipedia": [
    "superabundant number"
  ],
  "word": "superabundant number"
}