A260850 Lexicographically earliest sequence such that for any n>1, n=u*v, where u/v = a(n)/a(n-1) in reduced form.

1, 2, 6, 24, 120, 20, 140, 1120, 10080, 1008, 11088, 924, 12012, 858, 1430, 22880, 388960, 1750320, 33256080, 1662804, 3879876, 176358, 4056234, 10816624, 270415600, 10400600, 280816200, 10029150, 290845350, 9694845, 300540195, 9617286240, 35263382880

Offset: 1

Author

Paul Tek, Aug 01 2015

Keywords

• nonn

Examples

			From _Michael De Vlieger_, Apr 12 2024: (Start)
Table showing exponents m of prime powers p^m | a(n), n = 1..20, with "." representing p < gpf(n) does not divide a(n):
                       1111
    n        a(n)  23571379
   ------------------------
    1          1   .
    2          2   1
    3          6   11
    4         24   31
    5        120   311
    6         20   2.1
    7        140   2.11
    8       1120   5.11
    9      10080   5211
   10       1008   42.1
   11      11088   42.11
   12        924   21.11
   13      12012   21.111
   14        858   11..11
   15       1430   1.1.11
   16      22880   5.1.11
   17     388960   5.1.111
   18    1750320   421.111
   19   33256080   421.1111
   20    1662804   22..1111 (End)
		

Links

• Paul Tek, Table of n, a(n) for n = 1..3365
• Paul Tek, PARI program for this sequence
• Michael De Vlieger, Plot p(i)^m(i) | a(n) at (x,y) = (n,i), n = 1..2048, 3X vertical exaggeration, with a color function showing m(i) = 1 in black, m(i) = 2 in red, ..., largest m(i) in the dataset in magenta.
• Michael De Vlieger, Prime Power Decomposition of a(n), n = 1..1000.

Crossrefs

Cf. A008336, A370974 (sorted version).

Programs

Mathematica

nn = 35; p[_] := 0; r = 0;
Do[(Map[If[p[#1] < #2,
      p[#1] += #2,
      p[#1] -= #2] & @@ # &, #];
      If[r < #, r = #] &[#[[-1, 1]] ] ) &@
    Map[{PrimePi[#1], #2} & @@ # &, FactorInteger[n]];
  a[n] = Times @@ Array[Prime[#]^p[#] &, r], {n, nn}];
Array[a, nn] (* Michael De Vlieger, Apr 12 2024 *)

PARI

\\ See Links section.

Formula

a(p) = p*a(p-1) for any prime p.

a(n) = A008336(n+1) for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 21, 22, 23; are there other indices with this property?