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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
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, 11, 12, 18, 11, 11, 33, 11, 11, 128, 65, 34, 20, 19, 19, 13, 13, 20, 13, 13, 34, 19, 19, 65, 19, 13, 13, 19, 256, 129, 66, 36, 35 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Subsequence of A162439.

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)!

LINKS

Table of n, a(n) for n=1..61.

FORMULA

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.

EXAMPLE

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.

MATHEMATICA

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 *)

CROSSREFS

Cf. A233564, A162439, A000120.

Sequence in context: A303354 A227418 A278447 * A069655 A004574 A073127

Adjacent sequences:  A235587 A235588 A235589 * A235591 A235592 A235593

KEYWORD

nonn,base

AUTHOR

Vladimir Shevelev, Jan 12 2014

STATUS

approved

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Last modified September 18 12:00 EDT 2019. Contains 327170 sequences. (Running on oeis4.)