

A235590


Sum of parts of the form 10...0 with nonnegative number of zeros in binary representation of csquarefree 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
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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_1k_21) + 2^(k_2k_31) + 2^(k_(r1)k_r1) + 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



