

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, 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
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OFFSET

0,3


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

Table of n, a(n) for n=0..29.
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.


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


CROSSREFS

Cf. A185021, A055634.
Sequence in context: A129356 A290344 A217858 * A055634 A133221 A232097
Adjacent sequences: A185272 A185273 A185274 * A185276 A185277 A185278


KEYWORD

nonn


AUTHOR

Bakir FARHI, Jan 21 2012


STATUS

approved



