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%I #18 Feb 15 2020 23:58:40
%S 1,1,2,1,2,2,3,2,2,2,4,2,4,2,4,4,2,2,8,2,4,4,8,4,4,8,4,4,6,4,12,2,4,4,
%T 8,16,8,2,4,8,8,2,24,4,16,32,8,2,8,4,16,8,8,2,20,24,4,8,8,8,32,2,4,32,
%U 4,32,24,4,4,16,16,2,8,4,8,64,4,16,12,2,4
%N Number of odd divisors of Lucas(n), Lucas numbers beginning at 2.
%C This is to A193292 as A000032 Lucas numbers (beginning at 2) is to A000045 Fibonacci numbers.
%H Amiram Eldar, <a href="/A193495/b193495.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = A001227(A000032(n)).
%e a(18) = 8 because L(18) = 5778 = 2 * 3^3 * 107 whose odd divisors are 8 in number: {1, 3, 9, 27, 107, 321, 963, 2889}. a(n) = 2 iff n is in A001606 (Indices of prime Lucas numbers).
%t Table[luc = LucasL[n]; r = IntegerExponent[luc, 2]; DivisorSigma[0, luc/2^r], {n, 0, 100}] (* _T. D. Noe_, Jul 29 2011 *)
%t Table[Count[Divisors[LucasL[n]],_?OddQ],{n,0,80}] (* _Harvey P. Dale_, Mar 28 2019 *)
%Y Cf. A000032, A001227, A001606, A193292.
%K nonn,easy
%O 0,3
%A _Jonathan Vos Post_, Jul 28 2011
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