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

1,2

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

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.

Example

See A260987.

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 *)

Prog

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

Crossrefs

Record high values of A008480.

Cf. A260987.

Sequence in context: A071611 A216453 A119500 * A348632 A365470 A110967

Adjacent sequences: A260630 A260631 A260632 * A260634 A260635 A260636

Keyword

nonn

Author

Gordon Hamilton, Nov 11 2015

Extensions

More terms from Michael De Vlieger, Nov 12 2015

Status

approved