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A260850
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Lexicographically earliest sequence such that for any n>1, n=u*v, where u/v = a(n)/a(n-1) in reduced form.
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1
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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
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OFFSET
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1,2
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LINKS
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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.
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FORMULA
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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?
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EXAMPLE
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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)
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MATHEMATICA
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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}], n];
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PROG
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(PARI) \\ See Links section.
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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