A195307 Where records occur in A129308 and also in A195155.

1, 2, 6, 12, 60, 180, 360, 420, 840, 1260, 2520, 5040, 13860, 27720, 55440, 83160, 166320, 277200, 360360, 720720, 1081080, 2162160, 2827440, 4324320, 6126120, 12252240, 24504480, 36756720, 73513440, 147026880, 183783600, 232792560, 367567200, 465585120, 698377680

Offset

1,2

Comments

Observation: a(n) ending at 0, if 5 <= n <= 24 and possibly more.

From David A. Corneth, Apr 14 2021: (Start)

Conjecture: for each term k > 1 in the sequence there exists prime p such that k/p is in the sequence.

From the first 35 terms only a(23) = 2827440 is not in A025487.

In the list of conjectured terms, if actual terms <= 10^16 are 97-smooth and have the following property: a(n+1) = a(n) + k*gcd(a(n), a(n-1), ..., a(n-20)) setting a(n) = 1 for n < 1 then those terms are actual terms.

The conjectured terms are 41-smooth and satisfy a(n+1) = a(n) + k*gcd(a(n), a(n-1), ..., a(n-13)). (End)

From Bernard Schott, Jul 30 2022: (Start)

Equivalently, integers whose number of oblong divisors (A129308) sets a new record.

Corresponding records of number of oblong divisors are 0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 12, 13, 14, ... (End)

Links

Table of n, a(n) for n=1..35.

David A. Corneth, Conjectured terms <= 10^16 (a(1)..a(35) are certain)

Example

a(4) = 12 is in the sequence because A129308(12) = 3 is larger than any earlier value in A129308. - Bernard Schott, Jul 30 2022

Crossrefs

Cf. A002378, A007862, A088726, A093687, A097212, A129308, A181826, A195155, A287142.

Sequence in context: A139315 A014767 A002319 * A101657 A104371 A104350

Adjacent sequences: A195304 A195305 A195306 * A195308 A195309 A195310

Keyword

nonn

Author

Omar E. Pol, Oct 16 2011

Extensions

More terms a(6)-a(24) from Alois P. Heinz, Oct 16 2011

a(25)-a(35) from David A. Corneth, Apr 14 2021

Status

approved