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%I #8 May 17 2024 01:45:35
%S 1,33,2295,5439,6699,7095,7497,7595,10241,11475,15345,19845,24651,
%T 25245,35845,37725,37791,49203,50463,51183,51471,60291,62073,64337,
%U 65569,66495,68313,78793,80223,81809,86031,98167,100659,103293,109395,115245,119067,119919,142137
%N Numbers k that divide the k-th little Schroeder number.
%C Numbers k such that k | A001003(k).
%H Amiram Eldar, <a href="/A372903/b372903.txt">Table of n, a(n) for n = 1..208</a>
%e 1 is a term since A001003(1) = 2 is divisible by 1.
%e 33 is a term since A001003(33) = 37836272668898230450209 = 33 * 1146553717239340316673 is divisible by 33.
%t seq[kmax_] := Module[{sc0 = 1, sc1 = 1, 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[10^5]
%o (PARI) lista(kmax) = {my(sc0 = 1, sc1 = 1, 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. A001003.
%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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