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%I #11 Nov 26 2019 04:18:34
%S 1,1,2,3,3,4,4,2,4,4,6,8,2,8,24,18,4,16,8,12,16,24,48,72,12,8,6,16,8,
%T 16,8,12,4,16,64,12,2,8,8,8,8,24,96,96,6,24,72,48,24,32,128,96,16,8,8,
%U 8,16,128,60,192,6,32,32,96,8,96,512,36,24,16,24,384,24,96,144,48,64,64,32
%N Number of divisors of Motzkin number A001006(n).
%H Amiram Eldar, <a href="/A152983/b152983.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = A000005(A001006(n)).
%e a(5)=4 because the Motzkin number M(5)=21 has 4 divisors: 1,3,7 and 21. - _Emeric Deutsch_, Jan 14 2009
%p with(numtheory): M := proc (n) options operator, arrow: (sum((-1)^j*binomial(n+1, j)*binomial(2*n-3*j, n), j = 0 .. floor((1/3)*n)))/(n+1) end proc: seq(tau(M(n)), n = 0 .. 82); # _Emeric Deutsch_, Jan 14 2009
%t mot[0] = 1; mot[n_] := mot[n] = mot[n - 1] + Sum[mot[k] * mot[n - 2 - k], {k, 0, n - 2}]; Table[DivisorSigma[0, mot[n]], {n, 0, 50}] (* _Amiram Eldar_, Nov 26 2019 *)
%Y Cf. A000005, A001006, A152763.
%K nonn
%O 0,3
%A _Omar E. Pol_, Dec 20 2008
%E Extended by _Emeric Deutsch_, Jan 14 2009
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