OFFSET
1,1
COMMENTS
The sequence is not periodic, values of numerators are always -1+2^s.
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
FORMULA
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
EXAMPLE
a(3) = sigma(72)/sigma(36) = 15/7.
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, ...
MATHEMATICA
Table[Numerator[DivisorSigma[1, 8n^2]/DivisorSigma[1, 4n^2]], {n, 70}] (* Harvey P. Dale, Mar 21 2018 *)
PROG
(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
(PARI) a(n)=2^(2*valuation(n, 2)+4)-1 \\ Charles R Greathouse IV, Nov 17 2015
(Magma)
A065915:= func< n | 2^(2*Valuation(n, 2)+4) -1 >;
[A065915(n): n in [1..100]]; // G. C. Greubel, Aug 25 2024
(SageMath)
def A065915(n): return 2^(2*valuation(n, 2)+4) -1
[A065915(n) for n in range(1, 101)] # G. C. Greubel, Aug 25 2024
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Labos Elemer, Nov 28 2001
STATUS
approved