A349100 a(n) is the product of the Fibonacci divisors of A129655(n) that do not divide A129655(n-1).

1, 2, 3, 8, 5, 144, 21, 55, 13, 34, 2584, 377, 6765, 46368, 507544400, 46368, 987, 89, 17711, 233, 317811, 2932589884016, 317811, 14930352, 121393, 1597, 102334155, 4807526976, 2178309, 1548008755920, 5702887, 4181, 196418, 86267571272

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 A129655(15) and A129655(22), there are two new Fibonacci divisor. [updated by Max Alekseyev, Jun 16 2026]

Relatedly and remarkably, we have a(16) = a(14) and a(23) = a(21). - Max Alekseyev, Jun 16 2026

Links

Table of n, a(n) for n=1..34.

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, A356063.

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

Extensions

Edited and a(15)-a(34) added by Max Alekseyev, Jun 23 2026

Status

approved