login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%I

%S 1,1,3,3,15,15,105,105,945,945,10395,3465,45045,45045,675675,675675,

%T 11486475,11486475,218243025,43648605,916620705,916620705,21082276215,

%U 2342475135,58561878375,58561878375,1581170716125,225881530875,6550564395375,6550564395375

%N 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).

%C 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.

%H B. Farhi, <a href="https://arxiv.org/abs/1004.2269">A study of a curious arithmetic function</a>, arXiv:1004.2269 [math.NT], April 13 2010.

%H Bakir Farhi, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Farhi/farhi3.html">A Study of a Curious Arithmetic Function</a>, Journal of Integer Sequences, Vol. 15 (2012), #12.3.1.

%F 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

%Y Cf. A185021, A055634.

%K nonn

%O 0,3

%A _Bakir FARHI_, Jan 21 2012

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 7 12:05 EDT 2021. Contains 343650 sequences. (Running on oeis4.)