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

%I A260850 #31 Jun 27 2025 02:24:11
%S A260850 1,2,6,24,120,20,140,1120,10080,1008,11088,924,12012,858,1430,22880,
%T A260850 388960,1750320,33256080,1662804,3879876,176358,4056234,10816624,
%U A260850 270415600,10400600,280816200,10029150,290845350,9694845,300540195,9617286240,35263382880
%N A260850 Lexicographically earliest sequence such that for any n>1, n=u*v, where u/v = a(n)/a(n-1) in reduced form.
%H A260850 Paul Tek, <a href="/A260850/b260850.txt">Table of n, a(n) for n = 1..3365</a>
%H A260850 Paul Tek, <a href="/A260850/a260850.txt">PARI program for this sequence</a>
%H A260850 Michael De Vlieger, <a href="/A260850/a260850.png">Plot p(i)^m(i) | a(n) at (x,y) = (n,i)</a>, 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.
%H A260850 Michael De Vlieger, <a href="/A260850/a260850_1.txt">Prime Power Decomposition of a(n)</a>, n = 1..1000.
%F A260850 a(p) = p*a(p-1) for any prime p.
%F A260850 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?
%e A260850 From _Michael De Vlieger_, Apr 12 2024: (Start)
%e A260850 Table showing exponents m of prime powers p^m | a(n), n = 1..20, with "." representing p < gpf(n) does not divide a(n):
%e A260850                        1111
%e A260850     n        a(n)  23571379
%e A260850    ------------------------
%e A260850     1          1   .
%e A260850     2          2   1
%e A260850     3          6   11
%e A260850     4         24   31
%e A260850     5        120   311
%e A260850     6         20   2.1
%e A260850     7        140   2.11
%e A260850     8       1120   5.11
%e A260850     9      10080   5211
%e A260850    10       1008   42.1
%e A260850    11      11088   42.11
%e A260850    12        924   21.11
%e A260850    13      12012   21.111
%e A260850    14        858   11..11
%e A260850    15       1430   1.1.11
%e A260850    16      22880   5.1.11
%e A260850    17     388960   5.1.111
%e A260850    18    1750320   421.111
%e A260850    19   33256080   421.1111
%e A260850    20    1662804   22..1111 (End)
%t A260850 nn = 35; p[_] := 0; r = 0;
%t A260850 Do[(Map[If[p[#1] < #2,
%t A260850       p[#1] += #2,
%t A260850       p[#1] -= #2] & @@ # &, #];
%t A260850       If[r < #, r = #] &[#[[-1, 1]] ] ) &@
%t A260850     Map[{PrimePi[#1], #2} & @@ # &, FactorInteger[n]];
%t A260850   a[n] = Times @@ Array[Prime[#]^p[#] &, r], {n, nn}];
%t A260850 Array[a, nn] (* _Michael De Vlieger_, Apr 12 2024 *)
%o A260850 (PARI) \\ See Links section.
%Y A260850 Cf. A008336, A370974 (sorted version).
%K A260850 nonn
%O A260850 1,2
%A A260850 _Paul Tek_, Aug 01 2015