See abundant number in All languages combined, or Wiktionary
Download JSON data for abundant number meaning in English (4.1kB)
{
"forms": [
{
"form": "abundant numbers",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "abundant number (plural abundant numbers)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
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"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Number theory",
"orig": "en:Number theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"derived": [
{
"word": "extremely abundant number"
},
{
"word": "highly abundant number"
},
{
"word": "superabundant number"
}
],
"examples": [
{
"text": "The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30, and 1 + 2 + 3 + 5 + 6 + 10 + 15 = 42, which is greater than 30, so 30 is an abundant number."
},
{
"ref": "1970, Geometric Transformations III, Random House, page 128",
"text": "It has been shown that the largest odd number which cannot be written as the sum of two abundant numbers is 20161.",
"type": "quotation"
},
{
"text": "1992, Stanley Rabinowitz (editor), Index to Mathematical Problems, 1980-1984, MathPro Press, page 185,\n(a) Let k be fixed. Do there exist sequences of k consecutive abundant numbers?"
},
{
"ref": "1996, Richard R. Hall, Sets of Multiples, Cambridge University Press, page xi",
"text": "We shall not be concerned with abundant numbers in this book, nevertheless it may be helpful to use this historical example as an illustration. We note the property that any multiple of an abundant number is abundant.",
"type": "quotation"
}
],
"glosses": [
"A number that is less than the sum of its proper divisors (all divisors except the number itself)."
],
"hyponyms": [
{
"sense": "number that is less than the sum of its proper divisors",
"word": "weird number"
}
],
"id": "en-abundant_number-en-noun-hI42L20e",
"links": [
[
"number theory",
"number theory"
],
[
"proper",
"proper"
],
[
"divisor",
"divisor"
]
],
"raw_glosses": [
"(number theory) A number that is less than the sum of its proper divisors (all divisors except the number itself)."
],
"related": [
{
"word": "abundance"
},
{
"word": "abundancy index"
},
{
"word": "amicable number"
},
{
"word": "deficient number"
},
{
"word": "perfect number"
},
{
"word": "semiperfect number"
},
{
"word": "sociable number"
}
],
"synonyms": [
{
"tags": [
"excessive",
"numeral"
],
"word": "number that is less than the sum of its proper divisors"
}
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "number that is less than the sum of its proper divisors",
"word": "runsas luku"
},
{
"code": "fr",
"lang": "French",
"sense": "number that is less than the sum of its proper divisors",
"tags": [
"masculine"
],
"word": "nombre abondant"
},
{
"code": "it",
"lang": "Italian",
"sense": "number that is less than the sum of its proper divisors",
"tags": [
"masculine"
],
"word": "numero abbondante"
},
{
"code": "es",
"lang": "Spanish",
"sense": "number that is less than the sum of its proper divisors",
"tags": [
"masculine"
],
"word": "número abundante"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "number that is less than the sum of its proper divisors",
"tags": [
"neuter"
],
"word": "ymnigt tal"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "number that is less than the sum of its proper divisors",
"tags": [
"neuter"
],
"word": "rikt tal"
}
],
"wikipedia": [
"abundant number"
]
}
],
"sounds": [
{
"ipa": "/əˈbʌn.dn̩t ˈnʌm.bə/",
"tags": [
"Received-Pronunciation"
]
},
{
"ipa": "/əˈbʌn.dn̩t ˈnʌm.bɚ/",
"tags": [
"US"
]
},
{
"ipa": "/əˈbn̩.dn̩t ˈnʌm.bɚ/",
"tags": [
"US"
]
},
{
"audio": "LL-Q1860 (eng)-Persent101-abundant number.wav",
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"tags": [
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"text": "Audio (US)"
}
],
"word": "abundant number"
}
{
"derived": [
{
"word": "extremely abundant number"
},
{
"word": "highly abundant number"
},
{
"word": "superabundant number"
}
],
"forms": [
{
"form": "abundant numbers",
"tags": [
"plural"
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"args": {},
"expansion": "abundant number (plural abundant numbers)",
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{
"sense": "number that is less than the sum of its proper divisors",
"word": "weird number"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "abundance"
},
{
"word": "abundancy index"
},
{
"word": "amicable number"
},
{
"word": "deficient number"
},
{
"word": "perfect number"
},
{
"word": "semiperfect number"
},
{
"word": "sociable number"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with IPA pronunciation",
"English terms with audio links",
"English terms with quotations",
"en:Number theory"
],
"examples": [
{
"text": "The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30, and 1 + 2 + 3 + 5 + 6 + 10 + 15 = 42, which is greater than 30, so 30 is an abundant number."
},
{
"ref": "1970, Geometric Transformations III, Random House, page 128",
"text": "It has been shown that the largest odd number which cannot be written as the sum of two abundant numbers is 20161.",
"type": "quotation"
},
{
"text": "1992, Stanley Rabinowitz (editor), Index to Mathematical Problems, 1980-1984, MathPro Press, page 185,\n(a) Let k be fixed. Do there exist sequences of k consecutive abundant numbers?"
},
{
"ref": "1996, Richard R. Hall, Sets of Multiples, Cambridge University Press, page xi",
"text": "We shall not be concerned with abundant numbers in this book, nevertheless it may be helpful to use this historical example as an illustration. We note the property that any multiple of an abundant number is abundant.",
"type": "quotation"
}
],
"glosses": [
"A number that is less than the sum of its proper divisors (all divisors except the number itself)."
],
"links": [
[
"number theory",
"number theory"
],
[
"proper",
"proper"
],
[
"divisor",
"divisor"
]
],
"raw_glosses": [
"(number theory) A number that is less than the sum of its proper divisors (all divisors except the number itself)."
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"wikipedia": [
"abundant number"
]
}
],
"sounds": [
{
"ipa": "/əˈbʌn.dn̩t ˈnʌm.bə/",
"tags": [
"Received-Pronunciation"
]
},
{
"ipa": "/əˈbʌn.dn̩t ˈnʌm.bɚ/",
"tags": [
"US"
]
},
{
"ipa": "/əˈbn̩.dn̩t ˈnʌm.bɚ/",
"tags": [
"US"
]
},
{
"audio": "LL-Q1860 (eng)-Persent101-abundant number.wav",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/94/LL-Q1860_%28eng%29-Persent101-abundant_number.wav/LL-Q1860_%28eng%29-Persent101-abundant_number.wav.mp3",
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"tags": [
"US"
],
"text": "Audio (US)"
}
],
"synonyms": [
{
"tags": [
"excessive",
"numeral"
],
"word": "number that is less than the sum of its proper divisors"
}
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "number that is less than the sum of its proper divisors",
"word": "runsas luku"
},
{
"code": "fr",
"lang": "French",
"sense": "number that is less than the sum of its proper divisors",
"tags": [
"masculine"
],
"word": "nombre abondant"
},
{
"code": "it",
"lang": "Italian",
"sense": "number that is less than the sum of its proper divisors",
"tags": [
"masculine"
],
"word": "numero abbondante"
},
{
"code": "es",
"lang": "Spanish",
"sense": "number that is less than the sum of its proper divisors",
"tags": [
"masculine"
],
"word": "número abundante"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "number that is less than the sum of its proper divisors",
"tags": [
"neuter"
],
"word": "ymnigt tal"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "number that is less than the sum of its proper divisors",
"tags": [
"neuter"
],
"word": "rikt tal"
}
],
"word": "abundant number"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-05 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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