This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A065915 #28 Dec 14 2024 20:31:10
%S A065915 15,63,15,255,15,63,15,1023,15,63,15,255,15,63,15,4095,15,63,15,255,
%T A065915 15,63,15,1023,15,63,15,255,15,63,15,16383,15,63,15,255,15,63,15,1023,
%U A065915 15,63,15,255,15,63,15,4095,15,63,15,255,15,63,15,1023,15,63,15,255,15,63
%N A065915 Numerator of sigma(8*n^2)/sigma(4*n^2).
%C A065915 The sequence is not periodic, values of numerators are always -1+2^s.
%H A065915 Harry J. Smith, <a href="/A065915/b065915.txt">Table of n, a(n) for n = 1..1000</a>
%F A065915 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 A065915 a(3) = sigma(72)/sigma(36) = 15/7.
%e A065915 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 A065915 Table[Numerator[DivisorSigma[1,8n^2]/DivisorSigma[1,4n^2]],{n,70}] (* _Harvey P. Dale_, Mar 21 2018 *)
%o A065915 (PARI) a(n) = numerator(sigma(8*n^2)/sigma(4*n^2)) \\ _Harry J. Smith_, Nov 04 2009
%o A065915 (PARI) a(n)=2^(2*valuation(n,2)+4)-1 \\ _Charles R Greathouse IV_, Nov 17 2015
%o A065915 (Magma)
%o A065915 A065915:= func< n | 2^(2*Valuation(n, 2)+4) -1 >;
%o A065915 [A065915(n): n in [1..100]]; // _G. C. Greubel_, Aug 25 2024
%o A065915 (SageMath)
%o A065915 def A065915(n): return 2^(2*valuation(n, 2)+4) -1
%o A065915 [A065915(n) for n in range(1,101)] # _G. C. Greubel_, Aug 25 2024
%Y A065915 Cf. A000203, A065916 (denominator).
%K A065915 nonn,easy,frac
%O A065915 1,1
%A A065915 _Labos Elemer_, Nov 28 2001