

A194086


Secondsmallest prime factor of the nth Lucas number (beginning with 2), if composite, or 1 otherwise.


0



1, 1, 1, 2, 1, 1, 3, 1, 1, 19, 41, 1, 7, 1, 281, 11, 1, 1, 3, 1, 2161, 29, 43, 461, 47, 101, 90481, 19, 14503, 19489, 3, 1, 4481, 199, 67, 29, 7, 1, 29134601, 79, 1601, 1, 3, 144481, 263, 11, 4969, 1, 769, 599786069, 41, 919, 103, 1, 3, 199, 10745088481, 229
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OFFSET

0,4


LINKS

Table of n, a(n) for n=0..57.


EXAMPLE

a(3) = 2 because the 3rd of the Lucas numbers (beginning at 2) is A000032(3) = 4 = 2^2, hence depending on whether one means by secondsmallest prime factor (i.e., distinct or not, with multiplicity or not) a(3) would be either 2 or 1.
a(10) is unambiguously 41, because L(10) = 123 = 3 * 41, and 41 is the secondsmallest prime factor, with no issues of multiplicity or distinctness.


MATHEMATICA

Table[f = FactorInteger[LucasL[n]]; If[Length[f] > 1, f[[2, 1]], If[Length[f] == 1 && f[[1, 2]] > 1, f[[1, 1]], 1]], {n, 0, 70}] (* T. D. Noe, Aug 15 2011 *)


CROSSREFS

Cf. A000032, A000040, A001606, A005479, A193615.
Sequence in context: A280698 A217667 A240850 * A164659 A057898 A094293
Adjacent sequences: A194083 A194084 A194085 * A194087 A194088 A194089


KEYWORD

nonn,easy


AUTHOR

Jonathan Vos Post, Aug 14 2011


STATUS

approved



