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

Author

Omar E. Pol, Oct 16 2011

Keywords

• nonn

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)

Examples

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

Links

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

Crossrefs

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

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