

A048672


Binary encoding of squarefree numbers (A005117) A048640[ n ]/2.


4



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

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 nth 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^(i11)+2^(i21)+...+2^(iz1), 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 * A127301 A209636 A122111
Adjacent sequences: A048669 A048670 A048671 * A048673 A048674 A048675


KEYWORD

easy,nonn


AUTHOR

Antti Karttunen, Jul 14 1999


STATUS

approved



