A349100 -id:A349100 - cp's OEIS frontend

A129655 Numbers that set a new record for number of Fibonacci divisors.

1, 2, 6, 24, 120, 720, 5040, 55440, 720720, 12252240, 232792560, 6750984240, 276790353840, 12732356276640, 523410559111440, 24076885719126240, 1131613628798933280, 100713612963105061920, 20042008979657907322080

Offset: 1

Jason Earls, May 19 2007

From Donovan Johnson, Jul 07 2009: (Start)
a(15) <= 598420745002080,
a(16) <= 36503665445126880,
a(17) <= 1131613628798933280,
a(18) <= 100713612963105061920. (End)
From Robert Israel, Sep 26 2019: (Start)
a(15) <= 523410559111440,
a(16) <= 24076885719126240. (End)
From David A. Corneth, Sep 27 2019: (Start)
a(19) <= 20042008979657907322080,
a(20) <= 4669788092260292406044640,
a(21) <= 1312210453925142166098543840,
a(22) <= 414821946023574034721351415840,
a(23) <= 116564966832624303756699747851040,
a(24) <= 37417354353272401505900619060183840,
a(25) <= 19494441618054921184574222530355780640,
a(26) <= 31132623264033709131765033380978181682080,
a(27) <= 67277598873576845433744237136293850614974880. (End)
From a(1) up to a(14), last known term, this sequence is equivalent to: a(n) is the smallest number that has exactly n Fibonacci divisors (A000045). The products of the new Fibonacci divisors that appear successively are in A349100. - Bernard Schott, Jul 15 2022

			5040 has 60 divisors with 7 of them being Fibonacci numbers, namely 1, 2, 3, 5, 8, 21 and 144.

J. Earls, Red Zen, Lulu Press, NY, 2006, p. 105.

David A. Corneth, Some actual values and some upper bounds on a(n), for n=1..134
David A. Corneth, PARI program

Cf. A000045, A005086, A035105, A349100.

a(n) <= A035105(n+1). - Daniel Suteu, Sep 27 2019

More terms from Donovan Johnson, Feb 26 2008
a(14) from Donovan Johnson, Jul 07 2009
a(15)-a(19) confirmed by David A. Corneth, Sep 06 2024

A356063 a(n) is the new Lucas divisor that appears at the step A356062(n).

Original entry on oeis.org

1, 2, 4, 3, 18, 7, 11, 76, 322, 29, 1364, 123, 47, 199, 24476, 843, 5778, 521

Offset: 1

Bernard Schott, Jul 25 2022

The sequence is not monotonic.

Conjecture: the sequence is well defined, i.e., it is not possible that two new Lucas divisors arrive while one disappears for some step in A356062.

			a(1) = 1 because the smallest integer that has only one Lucas divisor is 1 since 1 is the smallest Lucas number in A000032.
A356062(6) = 252 and the set of the six Lucas divisors of 252 is {1, 2, 3, 4, 7, 18}. Then, A356062(7) = 2772 and the set of the seven Lucas divisors of 2772 is {1, 2, 3, 4, 7, 11, 18}. The new Lucas divisor that appears in this set is 11, hence a(7) = 11.

Cf. A000032, A304092, A349100, A356062.

cp's OEIS Frontend

A129655 Numbers that set a new record for number of Fibonacci divisors.

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