A372472 Number of zeros in the binary expansion of the n-th squarefree number.

0, 1, 0, 1, 1, 0, 2, 1, 1, 1, 0, 3, 2, 2, 2, 1, 2, 1, 1, 0, 4, 4, 3, 3, 3, 2, 3, 3, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 1, 5, 5, 4, 4, 4, 3, 4, 4, 3, 3, 2, 4, 3, 3, 3, 2, 3, 2, 2, 2, 1, 4, 3, 3, 2, 3, 3, 2, 2, 2, 1, 3, 3, 2, 2, 1, 2, 1, 0, 6, 6, 5, 5, 5, 5, 5, 4, 4

Offset: 1

Author

Gus Wiseman, May 09 2024

Keywords

• nonn
• base

Examples

			The 12th squarefree number is 17, with binary expansion (1,0,0,0,1), so a(12) = 3.
		

Crossrefs

Positions of first appearances are A372473.

Restriction of A023416 to A005117.

For prime instead of squarefree we have A035103, ones A014499, bits A035100.

Counting 1's instead of 0's (so restrict A000120 to A005117) gives A372433.

For binary length we have A372475, run-lengths A077643.

A030190 gives binary expansion, reversed A030308.

A048793 lists positions of ones in reversed binary expansion, sum A029931.

A371571 lists positions of zeros in binary expansion, sum A359359.

A371572 lists positions of ones in binary expansion, sum A230877.

A372515 lists positions of zeros in reversed binary expansion, sum A359400.

Cf. A003714, A039004, A049093, A049094, A059015, A069010, A070939, A073642, A145037, A211997, A368494, A372474, A372516.

Programs

Maple

A372583 := proc(n)
    A023416(A005117(n)) ;
end proc:
seq(A372583(n),n=1..200) ; # R. J. Mathar, May 20 2024

Mathematica

DigitCount[Select[Range[100],SquareFreeQ],2,0]

Formula

a(n) = A023416(A005117(n)).

a(n) + A372433(n) = A070939(A005117(n)) = A372475(n).