A274333 - OEIS

%I #23 Sep 08 2022 08:46:17

%S 0,2,4,5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,24,26,27,28,30,31,

%T 33,36,37,38,41,47,49,53,54,56,61,62,66,68,70,71,72,76,78,79,80,86,90,

%U 91,96,110,113,117,120,121,136,140,144,164,168,172,178,202,203

%N Indices of Lucas numbers having exactly one primitive prime factor.

%C 0 together with numbers n such that A086600(n) = 1, except if n = 3.

%C The only primes in this sequence are the primes numbers in A001606, which gives the indices of prime Lucas numbers.

%H Arkadiusz Wesolowski, <a href="/A274333/b274333.txt">Table of n, a(n) for n = 1..102</a>

%o (Magma) lst:=[]; pr:=1; for n in [0..203] do pd:=PrimeDivisors(Lucas(n)); d:=1; t:=0; for c in [1..#pd] do f:=pd[c]; if Gcd(pr, f) eq 1 then t+:=1; else d:=d*f; end if; end for; if t eq 1 then Append(~lst, n); end if; pr:=pr*Truncate(Lucas(n)/d); end for; lst;

%Y Cf. A000032, A001606, A058036, A086600.

%K nonn

%O 1,2

%A _Arkadiusz Wesolowski_, Jun 22 2016