A152982 Sum of proper divisors of Motzkin number A001006(n).

0, 0, 1, 3, 4, 11, 21, 1, 37, 173, 1648, 3610, 1, 25125, 139086, 474576, 284493, 984021, 6536394, 24265740, 18678381, 96214041, 277799337, 1282283505, 2077807083, 1899874619, 19252363864, 44221482398, 1967547359, 29743945411, 1265868629

Offset

0,4

Links

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

Formula

a(n) = A001065(A001006(n)).

Example

a(6)=21 because A001006(6)=51, having as proper divisors 1, 3 and 17. - Emeric Deutsch, Dec 31 2008

Maple

with(numtheory): M := proc (n) options operator, arrow: sum(binomial(n, 2*k)*binomial(2*k, k)/(k+1), k = 0 .. n) end proc: seq(sigma(M(n))-M(n), n = 0 .. 30); # Emeric Deutsch, Dec 31 2008

Mathematica

mot[0] = 1; mot[n_] := mot[n] = mot[n - 1] + Sum[mot[k] * mot[n - 2 - k], {k, 0, n - 2}]; propDivSum[n_] := DivisorSigma[1, n] - n; Table[propDivSum[mot[n]], {n, 0, 30}] (* Amiram Eldar, Nov 26 2019 *)

Crossrefs

Cf. A001065, A001006, A152762, A152981, A152983.

Sequence in context: A049977 A000677 A110865 * A001642 A001643 A247171

Adjacent sequences: A152979 A152980 A152981 * A152983 A152984 A152985

Keyword

nonn

Author

Omar E. Pol, Dec 20 2008

Extensions

Extended by Emeric Deutsch, Dec 31 2008

Status

approved