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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

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: A229882 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 March 21 22:19 EDT 2019. Contains 321382 sequences. (Running on oeis4.)