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%I #21 Apr 04 2024 07:55:55
%S 15,63,15,255,15,63,15,1023,15,63,15,255,15,63,15,4095,15,63,15,255,
%T 15,63,15,1023,15,63,15,255,15,63,15,16383,15,63,15,255,15,63,15,1023,
%U 15,63,15,255,15,63,15,4095,15,63,15,255,15,63,15,1023,15,63,15,255,15,63
%N Numerator of sigma(8*n^2)/sigma(4*n^2).
%C The sequence is not periodic, values of numerators are always -1+2^s.
%H Harry J. Smith, <a href="/A065915/b065915.txt">Table of n, a(n) for n = 1..1000</a>
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A065916(n) = Sum_{k>=0} (2^(2*k+4)-1)/(2^(k+1)*(2^(2*k + 3)-1)) = 2.080617095034... . - _Amiram Eldar_, Apr 04 2024
%e a(3) = sigma(72)/sigma(36) = 15/7.
%e Fractions begin with 15/7, 63/31, 15/7, 255/127, 15/7, 63/31, 15/7, 1023/511, 15/7, 63/31, 15/7, 255/127, ...
%t Table[Numerator[DivisorSigma[1,8n^2]/DivisorSigma[1,4n^2]],{n,70}] (* _Harvey P. Dale_, Mar 21 2018 *)
%o (PARI) for (n=1, 1000, a=numerator(sigma(8*n^2)/sigma(4*n^2)); write("b065915.txt", n, " ", a)) \\ _Harry J. Smith_, Nov 04 2009
%o (PARI) a(n)=2^(2*valuation(n,2)+4)-1 \\ _Charles R Greathouse IV_, Nov 17 2015
%Y Cf. A000203, A065916 (denominator).
%K nonn,easy,frac
%O 1,1
%A _Labos Elemer_, Nov 28 2001
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