A372902 Numbers k that divide the k-th large Schröder number.

1, 2, 6, 33, 42, 154, 198, 258, 270, 342, 850, 1170, 1666, 1806, 2295, 2574, 3262, 3366, 3834, 4070, 4654, 4970, 5439, 6006, 6118, 6162, 6699, 7095, 7254, 7497, 7595, 10241, 11475, 12642, 14014, 15345, 17470, 17670, 18018, 19845, 22446, 23994, 24570, 24651, 25245, 25974, 26334

Offset: 1

Author

Amiram Eldar, May 16 2024

Keywords

• nonn

Comments

Numbers k such that k | A006318(k).

Examples

			2 is a term since A001850(2) = 6 = 2 * 3 is divisible by 2.
6 is a term since A001850(6) = 1806 = 6 * 301 is divisible by 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..434

Crossrefs

Cf. A006318.

Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).

Programs

Mathematica

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]

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);}