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A274353 Number of factors L(i) > 1 of A274280(n), where L = A000032 (Lucas numbers, 1,3,4,...)

%I A274353 #10 Mar 05 2018 04:56:57
%S A274353 1,1,1,1,1,2,1,2,2,1,2,2,1,2,2,1,2,3,2,2,1,2,3,2,2,2,1,2,3,2,3,2,3,2,
%T A274353 1,2,3,2,3,2,3,2,1,2,2,3,3,2,3,3,2,3,2,1,2,2,3,4,3,2,3,3,2,3,2,2,1,2,
%U A274353 3,2,3,4,3,2,3,3,3,2,3,3,2,2,1,2,3,2
%N A274353 Number of factors L(i) > 1 of A274280(n), where L = A000032 (Lucas numbers, 1,3,4,...)
%H A274353 G. C. Greubel, <a href="/A274353/b274353.txt">Table of n, a(n) for n = 1..1000</a>
%e A274353 The products of distinct Lucas numbers, arranged in increasing order, comprise A274280.  The list begins with 1, 3, 4, 7, 11, 12 = 3*4, so that a(6) = 2.
%t A274353 r[1] := 1; r[2] := 3; r[n_] := r[n] = r[n - 1] + r[n - 2];
%t A274353 s = {1}; z = 40; f = Map[r, Range[z]]; Take[f, 10]
%t A274353 Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}];
%t A274353 infQ[n_] := MemberQ[f, n];
%t A274353 a = Table[#[[Flatten[Position[Map[Apply[Times, #] &, #], s[[n]]]][[1]]]] &[
%t A274353 Rest[Subsets[Map[#[[1]] &, Select[Map[{#, infQ[#]} &,
%t A274353 Divisors[s[[n]]]], #[[2]] && #[[1]] > 1 &]]]]], {n, 2, 200}];
%t A274353 ans = Join[{{1}}, a]; Take[ans, 8]
%t A274353 w = Map[Length, ans] (* A274353 *)
%t A274353 Map[Apply[Times, #] &, Select[ans, Length[#] == 2 &]] (* A274347 *)
%t A274353 Map[Apply[Times, #] &, Select[ans, Length[#] == 3 &]] (* A274348 *)
%t A274353 (* _Peter J. C. Moses_, Jun 17 2016 *)
%Y A274353 Cf. A000032, A274280, A274347, A274348, A160009, A272947, A274354.
%K A274353 nonn,easy
%O A274353 1,6
%A A274353 _Clark Kimberling_, Jun 18 2016