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%I #8 May 17 2024 01:44:37
%S 1,2,6,18,54,66,162,198,486,594,726,1314,1458,1782,2178,2838,3222,
%T 3942,4374,5346,5778,5874,6534,7986,8514,8646,9666,11826,13122,14454,
%U 16038,17334,17622,19602,23958,25542,25938,28998,31218,35442,35478,39366,43362,48114
%N Numbers k that divide the k-th companion Pell number.
%C Numbers k such that k | A002203(k).
%H Amiram Eldar, <a href="/A372899/b372899.txt">Table of n, a(n) for n = 1..327</a>
%e 2 is a term since A002203(2) = 6 = 2 * 3 is divisible by 2.
%e 6 is a term since A002203(6) = 198 = 6 * 33 is divisible by 6.
%t Select[Range[50000], Divisible[LucasL[#, 2], #] &]
%o (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);}
%Y Cf. A002203.
%Y Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).
%K nonn
%O 1,2
%A _Amiram Eldar_, May 16 2024
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