A222208 -id:A222208 - cp's OEIS frontend

A222209 Inverse of permutation in A222208.

1, 3, 2, 5, 7, 4, 11, 9, 13, 17, 19, 6, 23, 29, 14, 15, 31, 8, 37, 21, 22, 41, 43, 10, 47, 53, 26, 25, 59, 28, 61, 27, 38, 67, 49, 12, 71, 73, 46, 35, 79, 33, 83, 57, 89, 97, 101, 18, 103, 51, 62, 69, 107, 16, 109, 55, 74, 113, 127, 34, 131, 137, 121, 45, 139

Offset: 1

Alois P. Heinz, Feb 12 2013

Permutation of the natural numbers A000027 with inverse permutation A222208.

Cf. A000027, A211384, A222208.

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a222209 = (+ 1) . fromJust . (`elemIndex` a222208_list)
-- Reinhard Zumkeller, Feb 13 2013

b:= proc(n) false end:
g:= proc(n) option remember; local h, i;
      if n<3 then h:= 2*n-1 else g(n-1); h:= ilcm(map(g,
         numtheory[divisors](n) minus {1, n})[]) fi;
      for i while b(i*h) do od;
      b(i*h):= true; i*h
    end:
a:= proc() local t, a; t, a:= -1, proc() -1 end;
      proc(n) local h;
        while a(n) = -1 do
          t:= t+1; h:= g(t);
          if a(h) = -1 then a(h):= t fi
        od; a(n)
      end
    end():
seq(a(n), n=1..100);

terms = 100; b[1] = 1; b[2] = 3; b[n_] := b[n] = Module[{d, s, c, k}, d = Divisors[n] ~Complement~ {1, n}; For[s = Sort[Array[b, n - 1]]; c = Complement[ Range[ Last[s]], s]; k = If[c == {}, Last[s] + 1, First[c]], True, k++, If[FreeQ[s, k], If[AllTrue[d, Divisible[k, b[#]] &], Return[k]]]]]; a[n_] := a[n] = For[k = 1, True, k++, If[b[k] == n, Return[k]]]; Array[a, terms] (* Jean-François Alcover, Feb 22 2018 *)

A242297 Record high values in A222208.

Original entry on oeis.org

1, 3, 6, 12, 18, 24, 36, 54, 72, 108, 162, 216, 324, 486, 540, 648, 720, 972, 1008, 1080, 1440, 1458, 1512, 2016, 2160, 4320, 5040, 6048, 8640, 12096, 12960, 30240, 40320, 50400, 60480, 80640, 100800, 129600, 136080, 181440, 226800, 272160, 403200, 408240

Offset: 1

J. Lowell, May 10 2014

nonn

RECORDS transform of A222208.

			4 is not in this sequence because 6 comes before 4 in A222208.

Alois P. Heinz, Table of n, a(n) for n = 1..100

Cf. A222208.

More terms from Alois P. Heinz, May 10 2014

A242211 a(1) = 4, a(n) = A222208(a(n-1)).

Original entry on oeis.org

4, 6, 12, 36, 144, 1296, 20736, 1679616, 429981696

Offset: 1

J. Lowell, May 07 2014

The definition "a(1) = 2, a(n) = A222208(a(n-1))" produces the periodic sequence 2, 3, 2, 3, 2, 3, 2, ... .
From Lechoslaw Ratajczak, May 23 2022: (Start)
It appears that a(n) = 2^(2^floor((n-1)/2))*3^(2^floor((n-2)/2)) (for n > 1). If it is true, a(10) = 2821109907456.
The definition "b(1) = 8, b(k) = A222208(b(k-1))" produces the sequence: 8, 18, 48, 324, 2304, 104976, ... . It appears that b(k) = 2^A135530(k-1)*3^A135530(k-2) (for k > 1). (End)

			a(3) = 12 because a(2) = 6 and A222208(6) = 12.

Cf. A222208, A222209.

a(8) from Alois P. Heinz, May 07 2014

a(9) from Sean A. Irvine, Jul 18 2022

A211384 a(1) = 1, a(2) = 3; for n>2, a(n) = smallest number > a(n-1) such that a(n) is divisible by a(d) for all divisors d of n.

Original entry on oeis.org

1, 3, 4, 6, 7, 12, 13, 18, 20, 21, 22, 24, 25, 39, 56, 72, 73, 120, 121, 126, 156, 198, 199, 216, 217, 225, 240, 312, 313, 336, 337, 360, 396, 438, 455, 480, 481, 726, 800, 882, 883, 936, 937, 990, 1120, 1194, 1195, 1296, 1300, 1302, 1460, 1800, 1801, 1920

Offset: 1

J. Lowell, Feb 07 2013

nonn

Conjecture: 10 and 25 are the only composite numbers n for which a(n) = a(n-1) + 1. - J. Lowell, Oct 03 2020

			a(6) = 12 is divisible by a(1) = 1, a(2) = 3, a(3) = 4.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A222208, A222209.

a:= proc(n) a(n):= `if`(n<3, 2*n-1, (h-> ceil((a(n-1)+1)/h)*h)
    (ilcm(map(a, numtheory[divisors](n) minus {1, n})[]))) end:
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 07 2013

a[1] = 1; a[2] = 3; a[n_] := a[n] = (Ceiling[(a[n-1]+1)/#]*#&)[LCM @@ Map[a, Most[Divisors[n]]]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Mar 27 2017, after Alois P. Heinz *)

More terms from Alois P. Heinz, Feb 07 2013

A242212 a(1) = 4. a(n) = A222209(a(n-1)).

Original entry on oeis.org

4, 5, 7, 11, 19, 37, 71, 151, 379, 1051, 3307, 11483, 44453

Offset: 1

J. Lowell, May 07 2014

Question: what is the smallest composite number > 4 in this sequence?

Cf. A222208, A222209.

a(13) from Alois P. Heinz, May 07 2014

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A222209 Inverse of permutation in A222208.

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A242297 Record high values in A222208.

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A242211 a(1) = 4, a(n) = A222208(a(n-1)).

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A211384 a(1) = 1, a(2) = 3; for n>2, a(n) = smallest number > a(n-1) such that a(n) is divisible by a(d) for all divisors d of n.

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A242212 a(1) = 4. a(n) = A222209(a(n-1)).

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