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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 (list; graph; refs; listen; history; text; internal format)
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 divide-and-conquer 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*n-1)*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^s-1, 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*n-1)*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

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Last modified October 18 18:58 EDT 2018. Contains 316323 sequences. (Running on oeis4.)