

A065916


Denominator of sigma(8*n^2)/sigma(4*n^2).


2



7, 31, 7, 127, 7, 31, 7, 511, 7, 31, 7, 127, 7, 31, 7, 2047, 7, 31, 7, 127, 7, 31, 7, 511, 7, 31, 7, 127, 7, 31, 7, 8191, 7, 31, 7, 127, 7, 31, 7, 511, 7, 31, 7, 127, 7, 31, 7, 2047, 7, 31, 7, 127, 7, 31, 7, 511, 7, 31, 7, 127, 7, 31, 7, 32767, 7, 31, 7, 127, 7, 31, 7, 511, 7
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OFFSET

1,1


COMMENTS

The sequence is not periodic. The denominators are always of the form 1+2^s.


LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000
R. Stephan, Some divideandconquer sequences ...
R. Stephan, Table of generating functions
Index entries for sequences related to binary expansion of n


FORMULA

From Johannes W. Meijer, Feb 12 2013: (Start)
a((2*n1)*2^p) = 2*4^(p+1)  1 for p >= 0 and n >= 1. Observe that a(2^p) = A083420(p+1).
a(2^(p+3)*n + 2^(p+2)  1) = a(2^(p+2)*n + 2^(p+1)  1) for p >= 0. (End)
a(n) = 2^s1, with s = 2*A007814(n) + 3. Recurrence: a(2n) = 4a(n)+3, a(2n+1) = 7.  Ralf Stephan, Aug 22 2013


EXAMPLE

sigma(72)/sigma(36) = 15/7, so a(3) = 7.


MAPLE

nmax:=73: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 1 to ceil(nmax/(p+2)) do a((2*n1)*2^p) := 2*4^(p+1)  1 od: od: seq(a(n), n=1..nmax); # Johannes W. Meijer, Feb 12 2013


PROG

(PARI) for (n=1, 1000, a=denominator(sigma(8*n^2)/sigma(4*n^2)); write("b065916.txt", n, " ", a) ) \\ Harry J. Smith, Nov 04 2009
(PARI) a(n)=2^(2*valuation(n, 2)+3)1 \\ Charles R Greathouse IV, Nov 18 2015


CROSSREFS

Cf. A000203, A028982, A065915, A220466.
Sequence in context: A196315 A156347 A221402 * A122654 A184121 A167768
Adjacent sequences: A065913 A065914 A065915 * A065917 A065918 A065919


KEYWORD

nonn,easy


AUTHOR

Labos Elemer, Nov 28 2001


STATUS

approved



