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A048672 Binary encoding of squarefree numbers (A005117) A048640[ n ]/2. 8
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 nonnegative integers. Note the indexing, the domain starts from 1, although the range includes also 0.

A246353 gives the inverse of this sequence, in a sense that a(A246353(n)) = n for all n >= 0, and A246353(a(n)) = n for all n >= 1. When one is subtracted from the latter, another permutation of nonnegative integers is obtained: A064273. - Antti Karttunen, Aug 23 2014 based on comment from 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

Inverse: A246353 (see also A064273).

Cf. A005117, A048639, A048640, A048623.

Cf. A019565.

Sequence in context: A120242 A054427 A232563 * A248513 A245613 A246166

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 October 21 23:13 EDT 2014. Contains 248381 sequences.