A227843 Numbers n such that the binary XOR of the divisors of n (A178910(n)) is a binary repunit (A000225).

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 2592, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 2458624, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592

Offset

1,2

Comments

These are also numbers n such that A178910(n) >= A178910(i) for all i<n.

All powers of 2 are in the sequence. Terms that are not 2^x are 2592 and 2458624. No other non-2^x terms below 2^35.

Links

Table of n, a(n) for n=1..36.

Mathematica

fQ[n_] := Union@ IntegerDigits[ Fold[ BitXor[#1, #2] &, 0, Divisors@ n], 2] == {1}; Select[ Range@ 1000000000, fQ] (* Robert G. Wilson v, Aug 22 2013 *)

Crossrefs

Cf. A000225, A178910.

Sequence in context: A234592 A168082 A295081 * A271482 A335890 A219531

Adjacent sequences: A227840 A227841 A227842 * A227844 A227845 A227846

Keyword

nonn,base

Author

Alex Ratushnyak, Jul 06 2013

Status

approved