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A256942 Number of odd squarefree numbers <= 2^n. 0
1, 1, 2, 4, 7, 13, 26, 52, 105, 209, 415, 830, 1661, 3321, 6641, 13279, 26565, 53123, 106237, 212488, 424973, 849945, 1699889, 3399761, 6799540, 13599124, 27198203, 54396423, 108792774, 217585510, 435171212, 870342371, 1740684723 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) + a(n+1) = A143658(n+1).

LINKS

Table of n, a(n) for n=0..32.

FORMULA

a(n) = sum(j=0..n, (-1)^j*A143658(n-j)).

a(n) = 2/3 * A143658(n) + 1/3 * sum(i=1..floor(2^(n/2)), A008683(i)*A065359(floor(2^n/i^2))).

EXAMPLE

For n=4 there are 7 odd squarefree numbers <= 2^4, namely 1,3,5,7,11,13,15.

MAPLE

g:= proc(n) option remember; local L ; L := convert(n, base, 2) ; (2*n - add( L[i]*(-1)^i, i=1..nops(L)))/3 ; end proc:

a:= n -> add(numtheory:-mobius(i)*g(floor(2^n/i^2)), i=1..floor(2^(n/2))):

seq(a(n), n=0..32);

CROSSREFS

Cf. A008683, A065359, A143658.

Sequence in context: A293314 A023431 A025246 * A112740 A309050 A265580

Adjacent sequences:  A256939 A256940 A256941 * A256943 A256944 A256945

KEYWORD

nonn

AUTHOR

Robert Israel, Apr 13 2015

STATUS

approved

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Last modified July 4 09:40 EDT 2020. Contains 335446 sequences. (Running on oeis4.)