

A048672


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


9



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 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 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


MATHEMATICA

Join[{0}, Total[2^(PrimePi[FactorInteger[#][[All, 1]]]  1)]& /@ Select[ Range[2, 100], SquareFreeQ]] (* JeanFrançois Alcover, Mar 15 2016 *)


PROG

(PARI) lista(nn) = {for (n=1, nn, if (issquarefree(n), if (n==1, x = 0, f = factor(n); x = sum(k=1, #f~, 2^(primepi(f[k, 1])1))); print1(x, ", "); ); ); } \\ Michel Marcus, Oct 02 2015


CROSSREFS

Inverse: A246353 (see also A064273).
Cf. A005117, A048639, A048640, A048623.
Cf. A019565.
Sequence in context: A120242 A054427 A232563 * A277517 A248513 A266414
Adjacent sequences: A048669 A048670 A048671 * A048673 A048674 A048675


KEYWORD

easy,nonn


AUTHOR

Antti Karttunen, Jul 14 1999


STATUS

approved



