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Search: id:A073675
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| A073675 |
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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. |
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+0
6
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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.
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
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LINKS
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Index entries for sequences that are permutations of the natural numbers
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FORMULA
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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
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CROSSREFS
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Sequence in context: A004488 A011419 A011133 this_sequence A156034 A160581 A021465
Adjacent sequences: A073672 A073673 A073674 this_sequence A073676 A073677 A073678
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 11 2002
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EXTENSIONS
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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
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