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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 14 07:29 EST 2019. Contains 329111 sequences. (Running on oeis4.)