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A235590 Sum of parts of the form 10...0 with nonnegative number of zeros in binary representation of c-squarefree numbers (A233564) as the corresponding powers of 2. 0

%I

%S 1,2,4,3,3,8,5,5,16,9,6,6,9,32,17,10,7,7,10,7,7,17,7,7,64,33,18,12,11,

%T 11,12,18,11,11,33,11,11,128,65,34,20,19,19,13,13,20,13,13,34,19,19,

%U 65,19,13,13,19,256,129,66,36,35

%N Sum of parts of the form 10...0 with nonnegative number of zeros in binary representation of c-squarefree numbers (A233564) as the corresponding powers of 2.

%C Subsequence of A162439.

%C The number of times of appearances of number k in the sequence is the number of compositions of k into distinct powers of 2, i.e., it is A000120(k)!

%F Let, for k_1>k_2>...>k_r, A233564(n) = 2^k_1 + 2^k_2 +...+ 2^k_r. Then a(n) = 2^(k_1-k_2-1) + 2^(k_2-k_3-1) + 2^(k_(r-1)-k_r-1) + 2^k_r.

%e Let n=17, A233564(17)=37. In binary a concatenation of parts of the form 10...0 which gives 37 is (100)(10)(1). Thus a(17)= 4+2+1 = 7.

%t bitPatt[n_]:=bitPatt[n]=Split[IntegerDigits[n,2],#2==0&]; Map[Plus@@(Map[FromDigits[#,2]&,bitPatt[#]])&,Select[Range[300],#==DeleteDuplicates[#]&[bitPatt[#]]&]] (* _Peter J. C. Moses_, Jan 15 2014 *)

%Y Cf. A233564, A162439, A000120.

%K nonn,base

%O 1,2

%A _Vladimir Shevelev_, Jan 12 2014

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Last modified October 20 20:13 EDT 2019. Contains 328272 sequences. (Running on oeis4.)