A372899 Numbers k that divide the k-th companion Pell number.

1, 2, 6, 18, 54, 66, 162, 198, 486, 594, 726, 1314, 1458, 1782, 2178, 2838, 3222, 3942, 4374, 5346, 5778, 5874, 6534, 7986, 8514, 8646, 9666, 11826, 13122, 14454, 16038, 17334, 17622, 19602, 23958, 25542, 25938, 28998, 31218, 35442, 35478, 39366, 43362, 48114

Offset: 1

Author

Amiram Eldar, May 16 2024

Keywords

• nonn

Comments

Numbers k such that k | A002203(k).

Examples

			2 is a term since A002203(2) = 6 = 2 * 3 is divisible by 2.
6 is a term since A002203(6) = 198 = 6 * 33 is divisible by 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..327

Crossrefs

Cf. A002203.

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

Programs

Mathematica

Select[Range[50000], Divisible[LucasL[#, 2], #] &]

PARI

lista(kmax) = {my(p1 = 2, p2 = 6, p3); print1("1, 2, "); for(k = 3, kmax, p3 = p1 + 2*p2; if(!(p3 % k), print1(k, ", ")); p1 = p2; p2 = p3);}