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%I #28 Dec 10 2018 09:11:37
%S 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,
%T 31,7,127,7,31,7,8191,7,31,7,127,7,31,7,511,7,31,7,127,7,31,7,2047,7,
%U 31,7,127,7,31,7,511,7,31,7,127,7,31,7,32767,7,31,7,127,7,31,7,511,7
%N Denominator of sigma(8*n^2)/sigma(4*n^2).
%C The sequence is not periodic. The denominators are always of the form -1+2^s.
%H Harry J. Smith, <a href="/A065916/b065916.txt">Table of n, a(n) for n = 1..1000</a>
%H R. Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences ...</a>
%H R. Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F From _Johannes W. Meijer_, Feb 12 2013: (Start)
%F 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).
%F a(2^(p+3)*n + 2^(p+2) - 1) = a(2^(p+2)*n + 2^(p+1) - 1) for p >= 0. (End)
%F 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
%e sigma(72)/sigma(36) = 15/7, so a(3) = 7.
%p 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
%o (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
%o (PARI) a(n)=2^(2*valuation(n,2)+3)-1 \\ _Charles R Greathouse IV_, Nov 18 2015
%Y Cf. A000203, A028982, A065915, A220466.
%K nonn,easy
%O 1,1
%A _Labos Elemer_, Nov 28 2001
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