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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. 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 Adjacent sequences: A260847 A260848 A260849 * A260851 A260852 A260853 KEYWORD nonn AUTHOR Paul Tek, Aug 01 2015 STATUS approved

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Last modified May 25 06:28 EDT 2024. Contains 372782 sequences. (Running on oeis4.)