login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A073675 Rearrangement of natural numbers such that a(n) is the smallest proper divisor of n not included earlier but if no such divisor exists then a(n) is the smallest proper multiple of n not included earlier, subject always to the condition that a(n) is not equal to n. 7
2, 1, 6, 8, 10, 3, 14, 4, 18, 5, 22, 24, 26, 7, 30, 32, 34, 9, 38, 40, 42, 11, 46, 12, 50, 13, 54, 56, 58, 15, 62, 16, 66, 17, 70, 72, 74, 19, 78, 20, 82, 21, 86, 88, 90, 23, 94, 96, 98, 25, 102, 104, 106, 27, 110, 28, 114, 29, 118, 120, 122, 31, 126, 128, 130, 33, 134, 136 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The parity of the sequence is E,D,E,E,E,D,E,E,E,D,E,E,E,D,E,E,E,D,E,E,E,D,..., that is, an D followed by three E's from the second term onwards.

Closely related to A035263: if A035263(n) = 1, a(n) = 2n; otherwise a(n)=n/2. - Franklin T. Adams-Watters, Feb 02 2006

This permutation is self-inverse. This is the case r=2 of sequences where a(n)=floor(n/r) if floor(n/r)>0 and not already in the sequence, a(n) = floor(n*r) otherwise. All such sequences (for r>=1) are permutations of the natural numbers. - Franklin T. Adams-Watters, Feb 06 2006

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Index entries for sequences that are permutations of the natural numbers

FORMULA

If multiplicity(n,2) is even, a(n) = 2n; otherwise a(n)=n/2, where multiplicity(n,2) = A007814(n) is the exponent of the highest power of 2 dividing n. - Franklin T. Adams-Watters, Feb 06 2006, Jul 31 2009

a(k*2^m) = k*2^(m+(-1)^m), m >= 0, odd k >= 1. - Carl R. White, Aug 23 2010

MAPLE

a:= proc(n) local i, m; m:=n;

      for i from 0 while irem(m, 2, 'r')=0 do m:=r od;

      m*2^`if`(irem(i, 2)=1, i-1, i+1)

    end:

seq(a(n), n=1..80);  # Alois P. Heinz, Feb 10 2014

MATHEMATICA

a[n_] := Module[{i, m = n}, For[i = 0, {q, r} = QuotientRemainder[m, 2]; r == 0, i++, m = q]; m*2^If[Mod[i, 2] == 1, i-1, i+1]]; Table[a[n], {n, 1, 80}] (* Jean-Fran├žois Alcover, Jun 10 2015, after Alois P. Heinz *)

PROG

(Other) /* GNU bc */ scale=0; for(n=1; n<=100; n++){m=0; for(k=n; !k%2; m++)k/=2; k*2^(m+(-1)^m)} [From Carl R. White, Aug 23 2010]

CROSSREFS

Matches A118967 for all non powers-of-two [From Carl R. White, Aug 23 2010]

Sequence in context: A011419 A011133 A197806 * A188167 A156034 A160581

Adjacent sequences:  A073672 A073673 A073674 * A073676 A073677 A073678

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Aug 11 2002

EXTENSIONS

More terms and comment from Franklin T. Adams-Watters, Feb 06 2006, Jul 31 2009

More terms from Franklin T. Adams-Watters, Feb 06 2006

Edited by N. J. A. Sloane, Jul 31 2009

Typo fixed by Charles R Greathouse IV, Apr 29 2010

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified November 20 04:05 EST 2017. Contains 294959 sequences.