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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.
5
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
1,2
LINKS
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.
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?
EXAMPLE
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)
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}], n];
Array[a, nn] (* Michael De Vlieger, Apr 12 2024 *)
PROG
(PARI) \\ See Links section.
CROSSREFS
Cf. A008336, A370974 (sorted version).
Sequence in context: A284567 A360300 A065422 * A008336 A360298 A033643
KEYWORD
nonn
AUTHOR
Paul Tek, Aug 01 2015
STATUS
approved