cp's OEIS Frontend

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

%I A372472 #8 May 20 2024 05:07:27
%S A372472 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,
%T A372472 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,
%U A372472 2,1,3,3,2,2,1,2,1,0,6,6,5,5,5,5,5,4,4
%N A372472 Number of zeros in the binary expansion of the n-th squarefree number.
%F A372472 a(n) = A023416(A005117(n)).
%F A372472 a(n) + A372433(n) = A070939(A005117(n)) = A372475(n).
%e A372472 The 12th squarefree number is 17, with binary expansion (1,0,0,0,1), so a(12) = 3.
%p A372472 A372583 := proc(n)
%p A372472     A023416(A005117(n)) ;
%p A372472 end proc:
%p A372472 seq(A372583(n),n=1..200) ; # _R. J. Mathar_, May 20 2024
%t A372472 DigitCount[Select[Range[100],SquareFreeQ],2,0]
%Y A372472 Positions of first appearances are A372473.
%Y A372472 Restriction of A023416 to A005117.
%Y A372472 For prime instead of squarefree we have A035103, ones A014499, bits A035100.
%Y A372472 Counting 1's instead of 0's (so restrict A000120 to A005117) gives A372433.
%Y A372472 For binary length we have A372475, run-lengths A077643.
%Y A372472 A030190 gives binary expansion, reversed A030308.
%Y A372472 A048793 lists positions of ones in reversed binary expansion, sum A029931.
%Y A372472 A371571 lists positions of zeros in binary expansion, sum A359359.
%Y A372472 A371572 lists positions of ones in binary expansion, sum A230877.
%Y A372472 A372515 lists positions of zeros in reversed binary expansion, sum A359400.
%Y A372472 Cf. A003714, A039004, A049093, A049094, A059015, A069010, A070939, A073642, A145037, A211997, A368494, A372474, A372516.
%K A372472 nonn,base
%O A372472 1,7
%A A372472 _Gus Wiseman_, May 09 2024