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

1,2

Comments

Numbers k such that k | A006318(k).

Links

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

Example

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.

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]

Prog

(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); }

Crossrefs

Cf. A006318.

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

Sequence in context: A118077 A013976 A213435 * A083666 A083126 A098960

Adjacent sequences: A372899 A372900 A372901 * A372903 A372904 A372905

Keyword

nonn

Author

Amiram Eldar, May 16 2024

Status

approved