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

Author

Omar E. Pol, Dec 20 2008

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

Formula

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

Extensions

Extended by Emeric Deutsch, Dec 31 2008