A019532 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A019532

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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

Table of n, a(n) for n=1..9.

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

MATHEMATICA

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

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.

Sequence in context: A346077 A335303 A337448 * A008537 A277195 A358208