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

0,3

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A000005, A001006, A152763.

Sequence in context: A226142 A063826 A320120 * A366121 A331377 A343754

Adjacent sequences: A152980 A152981 A152982 * A152984 A152985 A152986

Keyword

nonn

Author

Omar E. Pol, Dec 20 2008

Extensions

Extended by Emeric Deutsch, Jan 14 2009

Status

approved