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%I #27 Apr 15 2024 16:35:46
%S 1,2,6,24,120,20,140,1120,10080,1008,11088,924,12012,858,1430,22880,
%T 388960,1750320,33256080,1662804,3879876,176358,4056234,10816624,
%U 270415600,10400600,280816200,10029150,290845350,9694845,300540195,9617286240,35263382880
%N Lexicographically earliest sequence such that for any n>1, n=u*v, where u/v = a(n)/a(n-1) in reduced form.
%H Paul Tek, <a href="/A260850/b260850.txt">Table of n, a(n) for n = 1..3365</a>
%H Paul Tek, <a href="/A260850/a260850.txt">PARI program for this sequence</a>
%H 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 Michael De Vlieger, <a href="/A260850/a260850_1.txt">Prime Power Decomposition of a(n)</a>, n = 1..1000.
%F a(p) = p*a(p-1) for any prime p.
%F 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 From _Michael De Vlieger_, Apr 12 2024: (Start)
%e 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 1111
%e n a(n) 23571379
%e ------------------------
%e 1 1 .
%e 2 2 1
%e 3 6 11
%e 4 24 31
%e 5 120 311
%e 6 20 2.1
%e 7 140 2.11
%e 8 1120 5.11
%e 9 10080 5211
%e 10 1008 42.1
%e 11 11088 42.11
%e 12 924 21.11
%e 13 12012 21.111
%e 14 858 11..11
%e 15 1430 1.1.11
%e 16 22880 5.1.11
%e 17 388960 5.1.111
%e 18 1750320 421.111
%e 19 33256080 421.1111
%e 20 1662804 22..1111 (End)
%t nn = 35; p[_] := 0; r = 0;
%t Do[(Map[If[p[#1] < #2,
%t p[#1] += #2,
%t p[#1] -= #2] & @@ # &, #];
%t If[r < #, r = #] &[#[[-1, 1]] ] ) &@
%t Map[{PrimePi[#1], #2} & @@ # &, FactorInteger[n]];
%t a[n] = Times @@ Array[Prime[#]^p[#] &, r], {n, nn}], n];
%t Array[a, nn] (* _Michael De Vlieger_, Apr 12 2024 *)
%o (PARI) \\ See Links section.
%Y Cf. A008336, A370974 (sorted version).
%K nonn,changed
%O 1,2
%A _Paul Tek_, Aug 01 2015
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