OFFSET
1,1
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
EXAMPLE
a(1) = 240 = 2*3*5*8.
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=10^6; 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, k=h; While[ (d = F[k++]*c) < up, Sow@d ]]]]][[2, 1]]] (* Giovanni Resta, May 14 2016 *)
PROG
(PARI) list(lim)=my(v=List(), F, best=5, t2, t3, t4, j, k, l); while(fibonacci(best++)<=30*lim, ); F=vector(best, i, fibonacci(i)); for(i=6, best, j=4; while(j++<i && (t2=F[i]*F[j])<=6*lim, k=3; while(k++<j && (t3=t2*F[k])<=2*lim, l=2; while(l++<k && (t4=t3*F[l])<=lim, listput(v, t4))))); Set(v) \\ Charles R Greathouse IV, May 14 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 14 2016
STATUS
approved