A120255 Array read by rows, where the n-th row (of A120256(n) terms) lists the positive divisors, not occurring earlier in the array, of the n-th Fibonacci number.

1, 2, 3, 5, 4, 8, 13, 7, 21, 17, 34, 11, 55, 89, 6, 9, 12, 16, 18, 24, 36, 48, 72, 144, 233, 29, 377, 10, 61, 122, 305, 610, 47, 141, 329, 987, 1597, 19, 38, 68, 76, 136, 152, 323, 646, 1292, 2584, 37, 113, 4181, 15, 33, 41, 123, 165, 205, 451, 615, 1353, 2255, 6765, 26

Offset: 2

Author

Leroy Quet, Jun 13 2006

Keywords

• nonn
• tabf

Comments

A permutation of the natural numbers, ordered by A001177 and ties broken by the number itself. Inverse permutation is A119745. - Martin Fuller, Sep 10 2006

Examples

			Fibonacci(9) = 34; and the divisors of 34 are 1, 2, 17 and 34. Of these divisors, 1 and 2 occur earlier in the array.
So the 9th row of the array is [17, 34].
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 2..12333 (rows 2 <= n <= 100)

Crossrefs

Cf. A001177, A119745, A120256.

Programs

Mathematica

f[t_] := Append[t, Select[Divisors[Fibonacci[Length[t] + 1]], FreeQ[Flatten[t], # ] &]]; Flatten@Nest[f, {}, 20] (* Ray Chandler, Jun 14 2006 *)
DeleteDuplicates[Flatten[Divisors[Fibonacci[Range[30]]]]] (* Harvey P. Dale, Apr 13 2020 *)

Extensions

Extended by Ray Chandler, Jun 14 2006