A349100 a(n) is the product of the new Fibonacci divisors that appear when A129655(n) sets a new record for number of Fibonacci divisors.

1, 2, 3, 8, 5, 144, 21, 55, 13, 34, 2584, 377, 6765, 46368

Offset: 1

Author

Bernard Schott, Jul 16 2022

Keywords

• nonn
• more

Comments

As A129655(n) is also, up to A129655(14), the smallest integer that has exactly n Fibonacci divisors (A000045), a(n) from 1..14 is the new Fibonacci divisor that appears.

Kevin Ryde remarks that for two of the conjectured later terms of A129655, there are more than a single new Fibonacci divisor.

Examples

			A129655(1) = 1 because the smallest integer that has only one Fibonacci divisor is 1; the corresponding Fibonacci divisor is 1, so a(1) = 1.
A129655(6) = 720 and the set of the six Fibonacci divisors of 720 is {1, 2, 3, 5, 8, 144}. Then, A129655(7) = 5040 and the set of the seven Fibonacci divisors of 5040 is {1, 2, 3, 5, 8, 21, 144}. The new Fibonacci divisor that appears in this set is 21, hence a(7) = 21.
A129655(7) = 5040 and the set of the seven Fibonacci divisors of 5040 is {1, 2, 3, 5, 8, 21, 144}. Then A129655(8) = 55440 and the set of the eight Fibonacci divisors of 55040 is {1, 2, 3, 5, 8, 21, 55, 144}. The new Fibonacci divisor that appears is 55, hence a(8) = 55.
		

Crossrefs

Cf. A000045, A005086, A129655.