A372903 Numbers k that divide the k-th little Schroeder number.

1, 33, 2295, 5439, 6699, 7095, 7497, 7595, 10241, 11475, 15345, 19845, 24651, 25245, 35845, 37725, 37791, 49203, 50463, 51183, 51471, 60291, 62073, 64337, 65569, 66495, 68313, 78793, 80223, 81809, 86031, 98167, 100659, 103293, 109395, 115245, 119067, 119919, 142137

Offset: 1

Author

Amiram Eldar, May 16 2024

Keywords

• nonn

Comments

Numbers k such that k | A001003(k).

Examples

			1 is a term since A001003(1) = 2 is divisible by 1.
33 is a term since A001003(33) = 37836272668898230450209 = 33 * 1146553717239340316673 is divisible by 33.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..208

Crossrefs

Cf. A001003.

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

Programs

Mathematica

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]

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);}