A181156 Odd Fibonacci numbers F which have a proper Fibonacci divisor G such that F/G is a Lucas number or a product of Lucas numbers.

3, 21, 55, 377, 987, 6765, 17711, 121393, 317811, 2178309, 5702887, 39088169, 102334155, 701408733, 1836311903, 12586269025, 32951280099, 225851433717, 591286729879, 4052739537881, 10610209857723, 72723460248141, 190392490709135, 1304969544928657, 3416454622906707

Offset

1,1

Comments

A conjectural statement that, for odd prime p, the ratio F_{p^2}/F_{p} is never a Lucas number or a product of some Lucas numbers, yields that

a) an odd Fibonacci number F is in the sequence iff for its maximal proper Fibonacci divisor G, we have: ind G does not equal sqrt(ind F) and F/G does not have a proper Fibonacci divisor > 3;

b) an odd Fibonacci number F is in the sequence iff its index has one of the forms: 6k+2 or 6k+4 (see A047235).

Links

Table of n, a(n) for n=1..25.

Example

F = 3 has the proper Fibonacci divisor G=1, and F/G = 3 is a Lucas number.
F = 317811 has the proper Fibonacci divisors 3, 13, and 377, and F/377 = 843 is a Lucas number.

Crossrefs

Cf. A000045, A000032, A014437, A014447.

Sequence in context: A152773 A039595 A033567 * A356809 A162394 A129212

Adjacent sequences: A181153 A181154 A181155 * A181157 A181158 A181159

Keyword

nonn

Author

Vladimir Shevelev, Oct 07 2010

Status

approved