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A272947
Number of factors Fibonacci(i) > 1 of A160009(n+1).
6
1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 3, 1, 2, 2, 2, 3, 3, 1, 2, 2, 2, 2, 3, 3, 3, 1, 2, 2, 2, 2, 3, 3, 3, 3, 1, 4, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 1, 4, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 1, 4, 4, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3
OFFSET
1,6
EXAMPLE
A160009(15) = 30 = 2*3*5, so that a(15) = 3.
MATHEMATICA
s = {1}; nn = 60; f = Fibonacci[2 + Range[nn]]; Do[s = Union[s, Select[s*f[[i]], # <= f[[nn]] &]], {i, nn}]; s = Prepend[s, 0]; Take[s, 100] (* A160009 *)
isFibonacciQ[n_] := Apply[Or, Map[IntegerQ, Sqrt[{# + 4, # - 4} &[5 n^2]]]];
ans = Join[{{0}}, {{1}}, Table[#[[Flatten[Position[Map[Apply[Times, #] &, #], s[[n]]]][[1]]]] &[Rest[Subsets[Rest[Map[#[[1]] &, Select[Map[{#, isFibonacciQ[#]} &, Divisors[s[[n]]]], #[[2]] &]]]]]], {n, 3, 500}]]
Map[Length, ans] (* A272947 *)
Flatten[Position[Map[Length, ans], 1]] (* A272948 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 1 &]] (* A000045 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 2 &]] (* A271354 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 3 &]] (* A272949 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 4 &]] (* A272950 *)
(* Peter J. C. Moses, May 11 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 13 2016
STATUS
approved