A185275 Products of the first terms of the arithmetic sequence f(n) defined by f(2^k l) = l^{1 - k} (for k a nonnegative integer and l a positive odd integer).

1, 1, 3, 3, 15, 15, 105, 105, 945, 945, 10395, 3465, 45045, 45045, 675675, 675675, 11486475, 11486475, 218243025, 43648605, 916620705, 916620705, 21082276215, 2342475135, 58561878375, 58561878375, 1581170716125, 225881530875, 6550564395375, 6550564395375

Offset: 0

Author

Bakir FARHI, Jan 21 2012

Keywords

• nonn

Comments

Note that f(n) is not always an integer (for example f(12) = 1/3) but Farhi showed in his paper that the product Product_{i = 1..n} f(i) is always an integer.

Links

• B. Farhi, A study of a curious arithmetic function, arXiv:1004.2269 [math.NT], April 13 2010.
• Bakir Farhi, A Study of a Curious Arithmetic Function, Journal of Integer Sequences, Vol. 15 (2012), #12.3.1.

Crossrefs

Cf. A185021, A055634.

Formula

G.f.: G(0)/x -1/x, where G(k)= 1 + x*(2*k+1)/(1 - x/(x + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 07 2013