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 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. 14
 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 FORMULA If valuation(n,2) is even, a(n) = 2n; otherwise a(n)=n/2, where valuation(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-François Alcover, Jun 10 2015, after Alois P. Heinz *) PROG (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)} /* Carl R. White, Aug 23 2010 */ (PARI) a(n) = if (valuation(n, 2) % 2, n/2, 2*n); \\ Michel Marcus, Mar 17 2018 CROSSREFS Matches A118967 for all non-powers-of-two. - Carl R. White, Aug 23 2010 Row 2 and column 2 of A059897. 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

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Last modified September 24 18:11 EDT 2022. Contains 356949 sequences. (Running on oeis4.)