A019532 Numbers k such that Fibonacci(k) divides k!.

1, 2, 3, 4, 5, 6, 8, 12, 24

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

Comments

These terms m are called “triphobe” or “3-phobe” numbers, by the French website Diophante (see link), because there are no 3 positive integers b_1 < b_2 < b_3 such that b_1 divides b_2, b_2 divides b_3, and m = b_1 + b_2 + b_3. A number that is not “triphobe” is called “triphile” or “3-phile” (A160811). The set of k-phobe numbers is always finite, there exist 9 triphobe numbers and the largest one is 24. - Bernard Schott, Oct 23 2021

References

• Posting to math-fun(AT)cs.arizona.edu by R. W. Gosper Nov 06 1996.

Links

• Diophante, A496 - Pentaphiles et pentaphobes (in French).

Crossrefs

k-phobe numbers: this sequence (k=3), A348519 (k=4), A348520 (k=5).

k-phile numbers: A160811 \ {5} (k=3), A348517 (k=4), A348518 (k=5).

Cf. A000045, A000142, A160811.

Programs

Mathematica

Select[Range[30],Divisible[#!,Fibonacci[#]]&] (* Harvey P. Dale, Jun 14 2020 *)

Extensions

Offset changed to 1 by David A. Corneth, Oct 27 2021