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A137825
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Least number having the highest abundancy among numbers with exactly n factors (counted with multiplicity).
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1
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2, 6, 30, 60, 420, 4620, 13860, 180180, 360360, 6126120, 116396280, 2677114440, 77636318760, 155272637520, 776363187600, 24067258815600, 890488576177200, 2671465728531600, 109530094869795600, 4709794079401210800
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| "Least" is required in the definition, otherwise a(14) could be either 2*77636318760 or 5*77636318760, which have the same abundancy. It appears that only a(14) has this property. [From T. D. Noe (noe(AT)sspectra.com), Jan 24 2010]
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LINKS
| The Prime Glossary, Abundant Numbers.
Eric Weisstein's World of Mathematics, Abundancy.
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FORMULA
| a(n) = product of the first n terms of A137826. [From T. D. Noe (noe(AT)sspectra.com), Jan 24 2010]
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EXAMPLE
| a(4)=60 since it has four factors (2, 2, 3, 5) and its abundancy is 2.8; greater than any other number with four factors, i.e: 16 (1.93), 24 (2.5), 36 (2.52) and 210 (2.74).
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CROSSREFS
| Cf. A005101, A017665, A017666, A137826.
Sequence in context: A090801 A166062 A127517 * A008341 A174276 A117849
Adjacent sequences: A137822 A137823 A137824 * A137826 A137827 A137828
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KEYWORD
| easy,nonn
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AUTHOR
| Sergio Pimentel (ferdiego(AT)suddenlink.net), Feb 11 2008
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EXTENSIONS
| Edited by T. D. Noe, Jan 24 2010
Extended by T. D. Noe (noe(AT)sspectra.com), Jan 24 2010
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