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

Author

Alex Ratushnyak, Jul 06 2013

Keywords

• nonn
• base

Comments

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

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.

Crossrefs

Cf. A000225, A178910.

Programs

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 *)

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