A152983 Number of divisors of Motzkin number A001006(n).

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, 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, 8, 16, 128, 60, 192, 6, 32, 32, 96, 8, 96, 512, 36, 24, 16, 24, 384, 24, 96, 144, 48, 64, 64, 32

Offset: 0

Author

Omar E. Pol, Dec 20 2008

Keywords

• nonn

Examples

			a(5)=4 because the Motzkin number M(5)=21 has 4 divisors: 1,3,7 and 21. - _Emeric Deutsch_, Jan 14 2009
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000005, A001006, A152763.

Programs

Maple

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

Mathematica

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 *)

Formula

a(n) = A000005(A001006(n)).

Extensions

Extended by Emeric Deutsch, Jan 14 2009