cp's OEIS Frontend

A195307 Where records occur in A129308 and also in A195155.

%I A195307 #43 Jul 30 2022 12:41:28
%S A195307 1,2,6,12,60,180,360,420,840,1260,2520,5040,13860,27720,55440,83160,
%T A195307 166320,277200,360360,720720,1081080,2162160,2827440,4324320,6126120,
%U A195307 12252240,24504480,36756720,73513440,147026880,183783600,232792560,367567200,465585120,698377680
%N A195307 Where records occur in A129308 and also in A195155.
%C A195307 Observation: a(n) ending at 0, if 5 <= n <= 24 and possibly more.
%C A195307 From _David A. Corneth_, Apr 14 2021: (Start)
%C A195307 Conjecture: for each term k > 1 in the sequence there exists prime p such that k/p is in the sequence.
%C A195307 From the first 35 terms only a(23) = 2827440 is not in A025487.
%C A195307 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.
%C A195307 The conjectured terms are 41-smooth and satisfy a(n+1) = a(n) + k*gcd(a(n), a(n-1), ..., a(n-13)). (End)
%C A195307 From _Bernard Schott_, Jul 30 2022: (Start)
%C A195307 Equivalently, integers whose number of oblong divisors (A129308) sets a new record.
%C A195307 Corresponding records of number of oblong divisors are 0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 12, 13, 14, ... (End)
%H A195307 David A. Corneth, <a href="/A195307/a195307.gp.txt">Conjectured terms <= 10^16 (a(1)..a(35) are certain)</a>
%e A195307 a(4) = 12 is in the sequence because A129308(12) = 3 is larger than any earlier value in A129308. - _Bernard Schott_, Jul 30 2022
%Y A195307 Cf. A002378, A007862, A088726, A093687, A097212, A129308, A181826, A195155, A287142.
%K A195307 nonn
%O A195307 1,2
%A A195307 _Omar E. Pol_, Oct 16 2011
%E A195307 More terms a(6)-a(24) from _Alois P. Heinz_, Oct 16 2011
%E A195307 a(25)-a(35) from _David A. Corneth_, Apr 14 2021