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 A137825 Least number having the highest abundancy among numbers with exactly n prime factors (counted with multiplicity). 2
 2, 6, 30, 60, 420, 4620, 13860, 180180, 360360, 6126120, 116396280, 2677114440, 77636318760, 155272637520, 776363187600, 24067258815600, 890488576177200, 2671465728531600, 109530094869795600, 4709794079401210800, 221360321731856907600, 11732097051788416102800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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. - T. D. Noe, Jan 24 2010 No other terms through a(800000) have the above property. - Jon E. Schoenfield, Mar 02 2019 LINKS Jon E. Schoenfield, Table of n, a(n) for n = 1..373 The Prime Glossary, Abundant Numbers Jon E. Schoenfield, Magma program Eric Weisstein's World of Mathematics, Abundancy Xiaolong Wu, A New Type of Abundant Numbers, arXiv:1906.05796 [math.NT], 2019. See Table 1 p. 3. FORMULA a(n) = product of the first n terms of A137826. - T. D. Noe, Jan 24 2010 EXAMPLE a(4) = 2*2*3*5 = 60 since it has four factors and its abundancy is 2.8, which is greater than that of any other number with four factors; e.g., 2*2*2*2=16, 2*2*2*3=24, 2*2*3*3=36, and 2*3*5*7=210 have abundancies 1.9375, 2.5, 2.52777..., and 2.7428571..., respectively. PROG (Magma) See Schoenfield link. CROSSREFS Cf. A005101, A017665, A017666, A137826. Sequence in context: A325986 A298759 A127517 * A008341 A211889 A174276 Adjacent sequences:  A137822 A137823 A137824 * A137826 A137827 A137828 KEYWORD easy,nonn AUTHOR Sergio Pimentel, Feb 11 2008 EXTENSIONS Edited by T. D. Noe, Jan 24 2010 Extended by T. D. Noe, Jan 24 2010 a(21)-a(22) from Jon E. Schoenfield, Mar 02 2019 STATUS approved

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Last modified May 18 01:37 EDT 2021. Contains 343992 sequences. (Running on oeis4.)