A351714 - OEIS

%I #9 Mar 12 2022 12:13:53

%S 1,2,3,4,6,7,8,10,11,12,14,18,20,22,24,27,29,30,32,36,39,40,42,47,48,

%T 50,54,57,58,60,64,66,69,72,76,78,80,81,84,90,92,94,96,100,104,108,

%U 120,123,124,126,129,130,132,134,135,138,140,144,152,153,156,159,160

%N Lucas-Niven numbers: numbers that are divisible by the number of terms in their minimal (or greedy) representation in terms of the Lucas numbers (A130310).

%C Numbers k such that A116543(k) | k.

%H Amiram Eldar, <a href="/A351714/b351714.txt">Table of n, a(n) for n = 1..10000</a>

%e 6 is a term since its minimal Lucas representation, A130310(6) = 1001, has A116543(6) = 2 1's and 6 is divisible by 2.

%t lucasNivenQ[n_] := Module[{s = {}, m = n, k = 1}, While[m > 0, If[m == 1, k = 1; AppendTo[s, k]; m = 0, If[m == 2, k = 0; AppendTo[s, k]; m = 0, While[LucasL[k] <= m, k++]; k--; AppendTo[s, k]; m -= LucasL[k]; k = 1]]]; Divisible[n, Plus @@ IntegerDigits[Total[2^s], 2]]]; Select[Range[160], lucasNivenQ]

%Y Cf. A000032, A116543, A130310.

%Y Subsequences: A351715, A351716.

%Y Similar sequences: A005349, A049445, A064150, A064438, A064481, A118363, A328208, A328212, A331085, A333426, A342726, A334308, A331728, A342426, A344341, A351719.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Feb 17 2022