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%I #7 May 17 2024 01:45:19
%S 1,2,6,33,42,154,198,258,270,342,850,1170,1666,1806,2295,2574,3262,
%T 3366,3834,4070,4654,4970,5439,6006,6118,6162,6699,7095,7254,7497,
%U 7595,10241,11475,12642,14014,15345,17470,17670,18018,19845,22446,23994,24570,24651,25245,25974,26334
%N Numbers k that divide the k-th large Schröder number.
%C Numbers k such that k | A006318(k).
%H Amiram Eldar, <a href="/A372902/b372902.txt">Table of n, a(n) for n = 1..434</a>
%e 2 is a term since A001850(2) = 6 = 2 * 3 is divisible by 2.
%e 6 is a term since A001850(6) = 1806 = 6 * 301 is divisible by 6.
%t seq[kmax_] := Module[{sc0 = 1, sc1 = 2, sc2, s = {1}}, Do[sc2 = ((6*k-3)*sc1 - (k-2)*sc0)/(k+1); If[Divisible[sc2, k], AppendTo[s, k]]; sc0 = sc1; sc1 = sc2, {k, 2, kmax}]; s]; seq[27000]
%o (PARI) lista(kmax) = {my(sc0 = 1, sc1 = 2, sc2); print1(1, ", "); for(k = 2, kmax, sc2 = ((6*k-3)*sc1 - (k-2)*sc0)/(k+1); if(!(sc2 % k), print1(k, ", ")); sc0 = sc1; sc1 = sc2);}
%Y Cf. A006318.
%Y Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).
%K nonn
%O 1,2
%A _Amiram Eldar_, May 16 2024
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