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

1,6

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Example

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.

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 *)

Crossrefs

Cf. A000032, A274280, A274347, A274348, A160009, A272947, A274354.

Sequence in context: A143098 A225515 A265404 * A183028 A114284 A238303

Adjacent sequences: A274350 A274351 A274352 * A274354 A274355 A274356

Keyword

nonn,easy

Author

Clark Kimberling, Jun 18 2016

Status

approved