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

0,3

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