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

Author

Jason Earls, May 19 2007

Keywords

• nonn
• more

Comments

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

Examples

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

References

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

Links

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

Crossrefs

Cf. A000045, A005086, A035105, A349100.

Formula

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

Extensions

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