A274353 Number of factors L(i) > 1 of A274280(n), where L = A000032 (Lucas numbers, 1,3,4,...)
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, 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, 3, 2, 3, 4, 3, 2, 3, 3, 3, 2, 3, 3, 2, 2, 1, 2, 3, 2
Offset: 1
Examples
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.
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
r[1] := 1; r[2] := 3; r[n_] := r[n] = r[n - 1] + r[n - 2]; s = {1}; z = 40; f = Map[r, Range[z]]; Take[f, 10] Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}]; infQ[n_] := MemberQ[f, n]; a = Table[#[[Flatten[Position[Map[Apply[Times, #] &, #], s[[n]]]][[1]]]] &[ Rest[Subsets[Map[#[[1]] &, Select[Map[{#, infQ[#]} &, Divisors[s[[n]]]], #[[2]] && #[[1]] > 1 &]]]]], {n, 2, 200}]; ans = Join[{{1}}, a]; Take[ans, 8] w = Map[Length, ans] (* A274353 *) Map[Apply[Times, #] &, Select[ans, Length[#] == 2 &]] (* A274347 *) Map[Apply[Times, #] &, Select[ans, Length[#] == 3 &]] (* A274348 *) (* Peter J. C. Moses, Jun 17 2016 *)