A140459 - OEIS

A140459

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).

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

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..10000

EXAMPLE

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.

MATHEMATICA

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 *)

CROSSREFS

Sequence in context: A033157 A310574 A059659 * A319515 A139132 A295068

Adjacent sequences: A140456 A140457 A140458 * A140460 A140461 A140462

KEYWORD

base,nonn

AUTHOR

Leroy Quet, Jul 22 2008

EXTENSIONS

Extended beyond 32, R. J. Mathar, Aug 04 2008

STATUS

approved