cp's OEIS Frontend

A291834 First positions of records in A252665.

%I A291834 #8 Sep 03 2017 21:42:35
%S A291834 1,4,8,12,16,24,36,48,72,96,120,144,216,240,288,360,432,480,576,720,
%T A291834 1080,1440,2160,2520,2880,3600,4320,5040,7200,7560,8640,10080,14400,
%U A291834 15120,20160,25200,30240,40320,50400,60480,75600,80640,90720,100800,120960,151200,181440
%N A291834 First positions of records in A252665.
%C A291834 Distinct from A033833; first term not in A033833 is a(24) = 2520. There appear to be increasingly many terms a(n) not in A033833 as n increases.
%C A291834 The terms 2520, 7560, 25200, 221760, 665280, 8648640, ... are not in A033833 but are in A002182. The term 3600 is the smallest that is in neither A033833 nor A002182, but in A007416. The term 831600 is the smallest that is in none of the three aforementioned sequences.
%C A291834 Conjectures based on a(n) < 10^7:
%C A291834 1. Numbers in a(n) are products of the first several consecutive primes p.
%C A291834 2. Outside of a(1), the least prime factor of a(n) has multiplicity > 1. This implies no primes, primorials, or squarefree a(n) for n > 1.
%C A291834 3. The greatest prime factor of a(n) generally has multiplicity 1. Note, however, exceptions in a(n) for n = {1, 2, 3, 5, 7, 9, 12, 13, 15, 17, 19, 26, 29, 33, 73, ...}.
%C A291834 4. The multiplicities of prime factors p of m generally decrease or stay the same as p increases.
%C A291834 See "Records and first positions of records in A252665" for more information. - _Michael De Vlieger_, Sep 03 2017
%H A291834 Michael De Vlieger, <a href="/A291834/b291834.txt">Table of n, a(n) for n = 1..76</a>
%t A291834 With[{s = Array[f[#, #, 5] &, 10^4]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]]
%Y A291834 Cf. A002182, A007416, A033833, A252665, A291833.
%K A291834 nonn
%O A291834 1,2
%A A291834 _Michael De Vlieger_, Sep 03 2017