%I #13 Nov 26 2019 04:18:42

%S 0,0,1,3,4,11,21,1,37,173,1648,3610,1,25125,139086,474576,284493,

%T 984021,6536394,24265740,18678381,96214041,277799337,1282283505,

%U 2077807083,1899874619,19252363864,44221482398,1967547359,29743945411,1265868629

%N Sum of proper divisors of Motzkin number A001006(n).

%H Amiram Eldar, <a href="/A152982/b152982.txt">Table of n, a(n) for n = 0..200</a>

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

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

%p 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

%t 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 *)

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

%K nonn

%O 0,4

%A _Omar E. Pol_, Dec 20 2008

%E Extended by _Emeric Deutsch_, Dec 31 2008