A372901 Numbers k that divide the k-th central Delannoy number.

1, 3, 9, 21, 27, 81, 171, 189, 217, 243, 297, 351, 729, 903, 1547, 2187, 3591, 3661, 4131, 5499, 5967, 6019, 6561, 7533, 8001, 11997, 13203, 14217, 15309, 17181, 19683, 20601, 22113, 22599, 23529, 24297, 25659, 26163, 26319, 26487, 28441, 30051, 33021, 37179, 37791

Offset: 1

Author

Amiram Eldar, May 16 2024

Keywords

• nonn

Comments

Numbers k such that k | A001850(k).

Examples

			3 is a term since A001850(3) = 63 = 3 * 21 is divisible by 3.
9 is a term since A001850(9) = 1462563 = 9 * 162507 is divisible by 9.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..307

Crossrefs

Cf. A001850.

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

Programs

Mathematica

Select[Range[1000], Divisible[LegendreP[#, 3], #] &]

PARI

lista(kmax) = {my(cd0 = 1, cd1 = 3, cd2); print1("1, "); for(k = 2, kmax, cd2 = (3*(2*k-1)*cd1 - (k-1)*cd0)/k; if(!(cd2 % k), print1(k, ", ")); cd0 = cd1; cd1 = cd2);}