A274354 Number of factors L(i) > 1 of A274281(n), where L = A000032 (Lucas numbers, 2,1,3,4,..., with 1 excluded)

1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 3, 2, 1, 2, 2, 3, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 4, 3, 2, 2, 1, 2, 3, 2, 3, 3, 2, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 3, 3, 2, 3, 4, 3, 4, 2, 3, 2, 1, 2, 2, 3, 3, 2, 3, 3, 4, 3, 2, 3, 4, 3

Offset

1,4

Links

Table of n, a(n) for n=1..86.

Example

The products of distinct Lucas numbers (including 2, excluding 1), arranged in increasing order, comprise A274281 (with 1 removed).  The list begins with 2, 3, 4, 6 = 2*3, 7, 8 = 2*4, 11, 12, 14, 18, 21, 22, 24 = 2*3*4, so that a(4) = 2, a(6) = 2, a(13) = 3.

Mathematica

r[1] := 2; r[2] := 1; r[n_] := r[n] = r[n - 1] + r[n - 2];
s = {1}; z = 40; f = Join[{2}, Map[r, 2 + Range[z]]]; Take[f, 10]
Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}];
infQ[n_] := MemberQ[f, n];
ans = 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}];
Take[ans, 10]
w = Map[Length, ans]
Map[Apply[Times, #] &, Select[ans, Length[#] == 2 &]] (* A274349 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 3 &]] (* A274350 *)
(* Peter J. C. Moses, Jun 17 2016 *)

Crossrefs

Cf. A000032, A274353, A274349, A274350, A160009, A272947.

Sequence in context: A177740 A118458 A118459 * A083870 A368779 A052299

Adjacent sequences: A274351 A274352 A274353 * A274355 A274356 A274357

Keyword

nonn,easy

Author

Clark Kimberling, Jun 18 2016

Status

approved