See abundant number on Wiktionary
{
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"form": "abundant numbers",
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"pos": "noun",
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"word": "extremely abundant number"
},
{
"word": "highly abundant number"
},
{
"word": "superabundant number"
}
],
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{
"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": "quote"
},
{
"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": "quote"
}
],
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"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",
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"number theory",
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"(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"
}
],
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{
"tags": [
"excessive",
"numeral"
],
"word": "number that is less than the sum of its proper divisors"
}
],
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"mathematics",
"number-theory",
"sciences"
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{
"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",
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"sense": "number that is less than the sum of its proper divisors",
"tags": [
"neuter"
],
"word": "rikt tal"
}
],
"wikipedia": [
"abundant number"
]
}
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"ipa": "/əˈbʌn.dn̩t ˈnʌm.bə/",
"tags": [
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{
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"word": "abundant number"
}
{
"derived": [
{
"word": "extremely abundant number"
},
{
"word": "highly abundant number"
},
{
"word": "superabundant number"
}
],
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"form": "abundant numbers",
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{
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{
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{
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{
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{
"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": "quote"
},
{
"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": "quote"
}
],
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"(number theory) A number that is less than the sum of its proper divisors (all divisors except the number itself)."
],
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"sciences"
],
"wikipedia": [
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]
}
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],
"synonyms": [
{
"tags": [
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"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"
}
Download raw JSONL data for abundant number meaning in All languages combined (4.1kB)
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"section": "English",
"subsection": "noun",
"title": "abundant number",
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}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.