A372900 - OEIS

%I #8 May 17 2024 01:44:52

%S 1,6,12,52,390,650,663,2077,11479,31671,41158,43508,104894,123682,

%T 127370,170819,175075,191516,266247,274378,327159,341638,366903,

%U 383847,733985,1236087,1755063,1763775,2277964,2364654,3165126,6726156,7007823,7221084,10903815

%N Numbers k that divide the k-th term of Narayana's cows sequence.

%C Numbers k such that k | A000930(k).

%H Amiram Eldar, <a href="/A372900/b372900.txt">Table of n, a(n) for n = 1..43</a>

%e 6 is a term since A000930(6) = 6 is divisible by 6.

%e 12 is a term since A000930(12) = 60 = 5 * 12 is divisible by 12.

%t With[{m = 50000}, Position[LinearRecurrence[{1, 0, 1}, {1, 1, 2}, m]/Range[m], _?IntegerQ] // Flatten]

%o (PARI) lista(kmax) = {my(nc1 = 1, nc2 = 1, nc3 = 2, nc4); print1("1, "); for(k = 4, kmax, nc4 = nc1 + nc3; if(!(nc4 % k), print1(k, ", ")); nc1 = nc2; nc2 = nc3; nc3 = nc4);}

%Y Cf. A000930.

%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