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A048672 Binary encoding of squarefree numbers (A005117) A048640[ n ]/2. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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, 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

LINKS

Table of n, a(n) for n=1..53.

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = 2^(i1-1)+2^(i2-1)+...+2^(iz-1), where A005117[ n ] = p_i1*p_i2*p_i3*...*p_iz

MAPLE

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

CROSSREFS

Cf. A005117, A048639, A048640, A048623.

Cf. A019565.

Sequence in context: A120242 A054427 A232563 * A245613 A243493 A127301

Adjacent sequences:  A048669 A048670 A048671 * A048673 A048674 A048675

KEYWORD

easy,nonn

AUTHOR

Antti Karttunen, Jul 14 1999

STATUS

approved

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Last modified July 30 03:23 EDT 2014. Contains 245051 sequences.