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A048672
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Binary encoding of squarefree numbers (A005117) A048640[ n ]/2.
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4
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0, 1, 2, 4, 3, 8, 5, 16, 32, 9, 6, 64, 128, 10, 17, 256, 33, 512, 7, 1024, 18, 65, 12, 2048, 129, 34, 4096, 11, 8192, 257, 16384, 66, 32768, 20, 130, 513, 65536, 131072, 1025, 36, 19, 262144, 258, 13, 524288, 1048576, 2049, 24, 35, 2097152, 4097, 4194304, 68
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OFFSET
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1,3
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COMMENTS
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Permutation of A001477 (nonnegative integers). Shares with A048639 and A048623 the property that even numbers turn to odd encodings and vice versa.
Inverse of sequence A064273 considered as a permutation of the nonnegative integers. - Howard A. Landman (howard(AT)polyamory.org), Sep 25 2001
Also index of n-th term of A019565 when its terms are sorted in increasing order. For example: a(6) = 8. The smallest values of A019565 are 1,2,3,5,6,7 . The 6th is 7 which is A019565(8). - Philippe Lallouet (philip.lallouet(AT)orange.fr), Apr 28 2008
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LINKS
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Table of n, a(n) for n=1..53.
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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a(n) = 2^(i1-1)+2^(i2-1)+...+2^(iz-1), where A005117[ n ] = p_i1*p_i2*p_i3*...*p_iz
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MAPLE
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encode_sqrfrees := proc(upto_n) local b, i; b := [ ]; for i from 1 to upto_n do if(0 <> mobius(i)) then b := [ op(b), bef(i) ]; fi; od: RETURN(b); end; # see A048623 for bef
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CROSSREFS
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Cf. A005117, A048639, A048640, A048623.
Cf. A019565.
Sequence in context: A118783 A120242 A054427 * A127301 A209636 A122111
Adjacent sequences: A048669 A048670 A048671 * A048673 A048674 A048675
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KEYWORD
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easy,nonn
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AUTHOR
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Antti Karttunen, Jul 14 1999
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STATUS
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approved
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