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superabundant
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The answer SUPERABUNDANT has 7 possible clue(s) in existing crosswords.
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Definitions of superabundant in various dictionaries:
adj - most excessively abundant
Abundant to excess.
SUPERABUNDANT - In mathematics, a superabundant number (sometimes abbreviated as SA) is a certain kind of natural number. A natural number n is called superabundant ...
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Keep reading for additional results and analysis below.
| Possible Crossword Clues |
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| Extremely plentiful |
| Abnormally plentiful |
| Ban nude star sketchily covering up -- too common |
| Excessive in quality |
| Excessive in quantity |
| More than sufficient |
| Superabundant description |
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In mathematics, a superabundant number (sometimes abbreviated as SA) is a certain kind of natural number. A natural number n is called superabundant precisely when, for all m < n* * * * * * * σ * ( * m * ) * * m * * * < * * * * σ * ( * n * ) * * n * * * * * {\displaystyle {\frac {\sigma (m)}{m}}<{\frac {\sigma (n)}{n}}} * where σ denotes the sum-of-divisors function (i.e., the sum of all positive divisors of n, including n itself). The first few superabundant numbers are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ... (sequence A004394 in the OEIS). For example, the number 5 is not a superabundant number because for 1, 2, 3, 4, and 5, the sigma is 1, 3, 4, 7, 6, and 7/4 > 6/5. * Superabundant numbers were defined by Leonidas Alaoglu and Paul Erdős (1944). Unknown to Alaoglu and Erdős, about 30 pages of Ramanujan's 1915 paper "Highly Composite Numbers" were suppressed. Those pages were finally published in The Ramanujan Journal 1 (1997), 119–153. In section 59 of that paper, Ramanujan defines generalized highly composite numbers, which include the superabundant numbers. |