

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
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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



