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A127588
Maximal numerator of Product[(k/(k+1))^e(k),{k,1,n}] over all exponents e(k) equal to either 1 or -1.
1
2, 4, 16, 64, 128, 576, 4608, 16384, 64000, 640000, 2560000, 10240000, 54080000, 135200000, 1554251776, 24868028416, 49736056832, 557256278016, 2244339564544, 11075584000000, 74331795750912, 936622443986944, 7492979551895552, 85630228705050624
OFFSET
1,1
LINKS
R. de la Bretèche, C. Pomerance and G. Tenenbaum, Products of ratios of consecutive integers, Ramanujan J. 9 (2005) 131-138.
R. de la Bretèche, C. Pomerance and G. Tenenbaum, Products of ratios of consecutive integers, hal.archives-ouvertes.fr/hal-00091182
S. R. Finch, Products of consecutive-integer ratios, April 19, 2007. [Cached copy, with permission of the author]
J.-L. Nicolas, Nombres hautement composés, Acta Arith. 49 (1988) 395-412
J.-L. Nicolas, Some open questions, Ramanujan J. 9 (2005) 251-264
EXAMPLE
For n=6, (1/2)^(-1)*(2/3)^(-1)*(3/4)^(-1)*(4/5)*(5/6)^(-1)*(6/7) has, of all such products, the largest numerator 576.
CROSSREFS
Sequence in context: A138868 A138871 A001901 * A187822 A092585 A106186
KEYWORD
nonn
AUTHOR
Steven Finch, Apr 17 2007
EXTENSIONS
More terms from Robert G. Wilson v, Apr 24 2007
More terms from Goudout Élie, Dec 13 2013
Corrected by Goudout Élie, Dec 13 2013
STATUS
approved