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

1,2

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.

Links

Table of n, a(n) for n=1..14.

Example

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.

Sequence in context: A066570 A073656 A047930 * A073875 A356883 A377379

Adjacent sequences: A349097 A349098 A349099 * A349101 A349102 A349103

Keyword

nonn,more

Author

Bernard Schott, Jul 16 2022

Status

approved