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A152982
Sum of proper divisors of Motzkin number A001006(n).
3
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
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
KEYWORD
nonn
AUTHOR
Omar E. Pol, Dec 20 2008
EXTENSIONS
Extended by Emeric Deutsch, Dec 31 2008
STATUS
approved