%I #14 Dec 09 2020 03:06:48
%S 1,1,4,1,6,4,8,1,13,6,12,4,14,8,8,1,18,13,20,6,32,12,24,4,31,14,40,8,
%T 30,8,32,1,16,18,48,13,38,20,56,6,42,32,44,12,26,24,48,4,57,31,24,14,
%U 54,40,72,8,80,30,60,8,62,32,104,1,84,16,68,18,32,48,72
%N a(n) is the numerator of Sum_{odd d|n} 1/d.
%H Sumit Kumar Jha, <a href="https://arxiv.org/abs/2007.04243">An identity for the sum of inverses of odd divisors of n in terms of the number of representations of n as a sum of r squares</a>, arXiv:2007.04243 [math.GM], 2020.
%F a(n) = (-1)^(n+1) * A098986(n) for n>=1.
%e 1, 1, 4/3, 1, 6/5, 4/3, 8/7, 1, 13/9, 6/5, 12/11, 4/3, 14/13, 8/7, 8/5, 1, ...
%t a[n_] := Numerator @ DivisorSum[n, 1/# &, OddQ[#] &]; Array[a, 100] (* _Amiram Eldar_, Jul 09 2020 *)
%o (PARI) a(n) = numerator(sumdiv(n, d, if (d%2, 1/d)));
%Y Cf. A098985 (denominators), A098986.
%K nonn,frac
%O 1,3
%A _Michel Marcus_, Jul 09 2020