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

1, 6, 12, 24, 30, 60, 120, 180, 360, 720, 840, 1080, 1260, 1680, 2160, 2520, 4320, 5040, 7560, 10080, 12600, 15120, 25200, 30240, 45360, 50400, 60480, 75600, 90720, 110880, 120960, 151200, 226800, 277200, 302400, 453600, 604800, 665280, 831600, 907200

Offset: 1

Author

Gordon Hamilton, Nov 11 2015

Keywords

• nonn

Comments

If a prime is a divisor of a(n) it is also a divisor of a(n+1).

A260987(n) = A008480(a(n)). - Reinhard Zumkeller, Nov 18 2015

Hernane and Nicolas named these numbers h-champion numbers (the function h(n) is A008480). - Amiram Eldar, Aug 20 2019

Examples

			See A260987.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2011 (terms 1..80 from Reinhard Zumkeller)
• Marc Deléglise, Tables des 785 premiers champions de la fonction h(n), alternative link (pdf format).
• Mohand-Ouamar Hernane and Jean-Louis Nicolas, Grandes valeurs du nombre de factorisations d’un entier en produit ordonné de facteurs premiers, The Ramanujan Journal, Vol. 14, No. 2 (2007), pp. 277-304, alternative link.

Crossrefs

Record high values of A008480.

Cf. A260987.

Programs

Haskell

a260633 n = a260633_list !! (n-1)
-- where a260633_list is defined in A260987.
-- Reinhard Zumkeller, Nov 18 2015

Mathematica

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 *)

Extensions

More terms from Michael De Vlieger, Nov 12 2015