The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #18 Oct 17 2016 16:37:56
%S 0,0,1,4,6,10,20,1,36,172,2192,3371,1,22327,135561,517656,284492,
%T 933118,5446991,24265724,18238138,93800069,334654476,1368408363,
%U 2584589232,1823879615,25669818480,41583822879,1967330543,29409700520,1265785403,3239855363874
%N Arithmetic derivatives of the Motzkin numbers.
%F a(n) = A003415(A001006(n)).
%F a(n) = 1 for n in A092831.
%t Table[If[Abs@ # < 2, 0, # Total[#2/#1 & @@@ FactorInteger[Abs@ #]]] &@ Hypergeometric2F1[(1 - n)/2, -n/2, 2, 4], {n, 0, 31}] (* _Michael De Vlieger_, Oct 17 2016, after _Michael Somos_ at A003415 and _Peter Luschny_ at A001006 *)
%Y Cf. A003415, A001006, A068329, A092831.
%K nonn
%O 0,4
%A _Paul Bedard_, Oct 16 2016
%E More terms from _Alois P. Heinz_, Oct 16 2016