%I A073675
%S A073675 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,
%T A073675 54,56,58,15,62,16,66,17,70,72,74,19,78,20,82,21,86,88,90,23,94,96,98,
%U A073675 25,102,104,106,27,110,28,114,29,118,120,122,31,126,128,130,33,134,136
%N 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.
%C A073675 The parity of the sequence is E,O,E,E,E,O,E,E,E,O,E,E,E,O,E,E,E,O,E,E,
               E,O,..., that ism, an O followed by three E's from the second term 
               onwards.
%C A073675 Closely related to A035263: if A035263(n) = 1, a(n) = 2n; otherwise a(n)=n/
               2. - Franklin T. Adams-Watters, Feb 02 2006
%C A073675 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. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Feb 06 2006
%H A073675 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%F A073675 If multiplicity(n,2) is even, a(n) = 2n; otherwise a(n)=n/2, where multiplicity(n,
               2) = A07814(n) is the exponent of the highest power of 2 dividing 
               n. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 06 2006, 
               Jul 31 2009
%Y A073675 Sequence in context: A004488 A011419 A011133 this_sequence A156034 A160581 
               A021465
%Y A073675 Adjacent sequences: A073672 A073673 A073674 this_sequence A073676 A073677 
               A073678
%K A073675 nonn
%O A073675 1,1
%A A073675 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 11 2002
%E A073675 More terms and comment from Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Feb 06 2006, Jul 31 2009
%E A073675 More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 06 
               2006
%E A073675 Edited by N. J. A. Sloane, Jul 31 2009