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A260633 Numbers that set new records for the most ordered prime factorizations.

%I A260633 #34 Aug 24 2019 10:40:34
%S A260633 1,6,12,24,30,60,120,180,360,720,840,1080,1260,1680,2160,2520,4320,
%T A260633 5040,7560,10080,12600,15120,25200,30240,45360,50400,60480,75600,
%U A260633 90720,110880,120960,151200,226800,277200,302400,453600,604800,665280,831600,907200
%N A260633 Numbers that set new records for the most ordered prime factorizations.
%C A260633 If a prime is a divisor of a(n) it is also a divisor of a(n+1).
%C A260633 A260987(n) = A008480(a(n)). - _Reinhard Zumkeller_, Nov 18 2015
%C A260633 Hernane and Nicolas named these numbers h-champion numbers (the function h(n) is A008480). - _Amiram Eldar_, Aug 20 2019
%H A260633 Amiram Eldar, <a href="/A260633/b260633.txt">Table of n, a(n) for n = 1..2011</a> (terms 1..80 from Reinhard Zumkeller)
%H A260633 Marc Deléglise, <a href="http://math.univ-lyon1.fr/~deleglis/Calculs/hn21.txt">Tables des 785 premiers champions de la fonction h(n)</a>, <a href="http://math.univ-lyon1.fr/homes-www/nicolas/table785.pdf">alternative link (pdf format)</a>.
%H A260633 Mohand-Ouamar Hernane and Jean-Louis Nicolas, <a href="https://doi.org/10.1007/s11139-007-9028-6">Grandes valeurs du nombre de factorisations d’un entier en produit ordonné de facteurs premiers</a>, The Ramanujan Journal, Vol. 14, No. 2 (2007), pp. 277-304, <a href="http://math.univ-lyon1.fr/homes-www/nicolas/hernane2.pdf">alternative link</a>.
%e A260633 See A260987.
%t A260633 t = {1}~Join~Array[Multinomial @@ Last@ Transpose@ FactorInteger@ # &, 5*10^6, 2]; m = {1}; a = {1}; Do[If[t[[k]] > Max@ m, AppendTo[m, t[[k]]]; AppendTo[a, k]], {k, 2, Length@ t}]; a (* _Michael De Vlieger_, Nov 12 2015, after _Olivier Gérard_ at A008480 *)
%o A260633 (Haskell)
%o A260633 a260633 n = a260633_list !! (n-1)
%o A260633 -- where a260633_list is defined in A260987.
%o A260633 -- _Reinhard Zumkeller_, Nov 18 2015
%Y A260633 Record high values of A008480.
%Y A260633 Cf. A260987.
%K A260633 nonn
%O A260633 1,2
%A A260633 _Gordon Hamilton_, Nov 11 2015
%E A260633 More terms from _Michael De Vlieger_, Nov 12 2015