A355758 Irregular triangle read by rows in which row n lists the divisors of n that are Fibonacci numbers.

1, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 3, 1, 1, 2, 8, 1, 3, 1, 2, 5, 1, 1, 2, 3, 1, 13, 1, 2, 1, 3, 5, 1, 2, 8, 1, 1, 2, 3, 1, 1, 2, 5, 1, 3, 21, 1, 2, 1, 1, 2, 3, 8, 1, 5, 1, 2, 13, 1, 3, 1, 2, 1, 1, 2, 3, 5, 1, 1, 2, 8, 1, 3, 1, 2, 34, 1, 5, 1, 2, 3, 1, 1, 2, 1, 3, 13, 1, 2, 5, 8

Offset: 1

Author

Michel Marcus, Jul 16 2022

Keywords

• nonn
• tabf

Examples

			Irregular triangle begins:
  1;
  1, 2;
  1, 3;
  1, 2;
  1, 5;
  1, 2, 3;
  1;
  1, 2, 8;
  1, 3;
  1, 2, 5;
  ...
		

Crossrefs

Cf. A000045, A010056.

Cf. A000012 (left border), A054494 (right border).

Cf. A005086 (row lengths), A005092 (row sums).

Subsequence of A027750.

Programs

Mathematica

With[{fib = Fibonacci[Range[2, 10]]}, row[n_] := Select[Divisors[n], MemberQ[fib, #] &]; Table[row[n], {n, 1, fib[[-1]]}] // Flatten] (* Amiram Eldar, Jul 16 2022 *)

PARI

isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8)); \\ A010056
row(n) = select(isfib, divisors(n));