|
| |
|
|
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.
|
|
6
| |
|
|
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; 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. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 06 2006
|
|
|
LINKS
| 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) = 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
a(k*2^m) = k*2^(m+(-1)^m), m >= 0, odd k >= 1 [From Carl R. White (oeisfan(AT)phodd.net), Aug 23 2010]
|
|
|
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 (oeisfan(AT)phodd.net), Aug 23 2010]
|
|
|
CROSSREFS
| Matches A118967 for all non powers-of-two [From Carl R. White (oeisfan(AT)phodd.net), 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 (amarnath_murthy(AT)yahoo.com), Aug 11 2002
|
|
|
EXTENSIONS
| More terms and comment from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 06 2006, Jul 31 2009
More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 06 2006
Edited by N. J. A. Sloane, Jul 31 2009
Typo fixed by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Apr 29 2010
|
| |
|
|
