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Numbers k that divide A005554(k) (the sum of consecutive Motzkin numbers).
1

%I #21 Jun 28 2022 02:50:13

%S 1,2,3,6,9,18,27,54,81,102,126,162,189,243,369,486,567,729,1071,1134,

%T 1323,1458,1462,1539,2187,2538,2889,3213,4374,4617,6561,7749,8262,

%U 8667,13122,14238,15498,19683,24786,27702,28994,32319,34263,39366,40838

%N Numbers k that divide A005554(k) (the sum of consecutive Motzkin numbers).

%C All the powers of 3 (A000244) are in the sequence.

%H Amiram Eldar, <a href="/A081741/b081741.txt">Table of n, a(n) for n = 1..165</a>

%t s = {1, 2}; k1 = 1; k2 = 2; Do[k3 = (2*n*k2 + (3*n - 9)*k1)/(n + 1); If[Divisible[k3, n], AppendTo[s, n]]; k1 = k2; k2 = k3, {n, 3, 42000}]; s (* _Amiram Eldar_, Jun 28 2022 *)

%Y Cf. A000244, A001006, A005554.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Apr 07 2003