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Numbers n such that the binary XOR of the divisors of n (A178910(n)) is a binary repunit (A000225).
2

%I #8 Aug 24 2013 02:18:25

%S 1,2,4,8,16,32,64,128,256,512,1024,2048,2592,4096,8192,16384,32768,

%T 65536,131072,262144,524288,1048576,2097152,2458624,4194304,8388608,

%U 16777216,33554432,67108864,134217728,268435456,536870912,1073741824,2147483648,4294967296,8589934592

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

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

%C 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.

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

%Y Cf. A000225, A178910.

%K nonn,base

%O 1,2

%A _Alex Ratushnyak_, Jul 06 2013