A272949 Products of three distinct Fibonacci numbers > 1.

30, 48, 78, 80, 120, 126, 130, 195, 204, 208, 210, 312, 315, 330, 336, 340, 504, 510, 520, 534, 544, 546, 550, 816, 819, 825, 840, 864, 880, 884, 890, 1320, 1326, 1335, 1360, 1365, 1398, 1424, 1428, 1430, 1440, 2136, 2142, 2145, 2160, 2184, 2200, 2210, 2262

Offset: 1

Author

Clark Kimberling, May 13 2016

Keywords

• nonn
• easy

Examples

			a(1) = 30 = 2*3*5.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A160009, A272947, A271354, A273950.

Programs

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 *)
up=10^9; F=Fibonacci; i=3; Union[ Reap[ While[(a = F[i++]) < up, j=i; While[ (b = F[j++]*a) < up, h=j; While[ (c = F[h++]*b) < up, Sow@c ]]]][[2, 1]]] (* Giovanni Resta, May 14 2016 *)