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A140459
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A positive integer n is included if n can be added to d(n) in binary without any carries, where d(n) is the number of positive divisors of n. In other words, no 1 in the binary representation of n is in the same position as any 1 in the binary representation of d(n).
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1
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4, 5, 8, 10, 13, 16, 17, 26, 27, 29, 32, 33, 34, 35, 36, 37, 41, 48, 51, 53, 54, 57, 58, 61, 64, 65, 66, 70, 73, 74, 80, 82, 89, 91, 96, 97, 100, 101, 102, 106, 109, 112, 113, 114, 115, 122, 123, 128, 129, 130, 135, 137, 144, 145, 146, 149, 153, 155, 157, 160, 161
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OFFSET
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1,1
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LINKS
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EXAMPLE
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27 in binary is 11011. 27 has 4 divisors. 4 in binary is 100. Comparing 11011 and 100, it is seen that the two do not have any ones in the same position, so 27 is included in the sequence.
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MATHEMATICA
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bcQ[n_]:=Module[{bd=IntegerDigits[n, 2], p}, p=PadLeft[IntegerDigits[ DivisorSigma[ 0, n], 2], Length[bd], 0]; Union[Pick[bd, p, 1]]=={0}]; Select[ Range[200], bcQ] (* Harvey P. Dale, Jan 26 2014 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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