The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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