A127588 Maximal numerator of Product[(k/(k+1))^e(k),{k,1,n}] over all exponents e(k) equal to either 1 or -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

Goudout Élie, Table of n, a(n) for n = 1..36

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

Adjacent sequences: A127585 A127586 A127587 * A127589 A127590 A127591

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