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%I #12 Aug 14 2019 12:53:54
%S 1,6,120,198,3696,6240,32640,56160,1941408,3592200,8119800,15628032,
%T 27125280,59032080,61788240,125859840,1635834720,2147450880,
%U 3709081680,16328199552,26198072160,52344970080,52396088160,209584184160,210197601120,236223190200,237385437360
%N Perfex numbers: n = binary XOR of divisors of n.
%C a(17) > 1e9.
%C 10^11 < a(24) <= 209584184160. a(25) <= 210197601120. - _Donovan Johnson_, Mar 12 2011
%C a(28) > 3*10^11. - _Giovanni Resta_, Aug 14 2019
%t lst = {}; k = 1; While[k < 10^9, If[ BitXor @@ Divisors@k == k, AppendTo[lst, k]; Print@k]; k++ ]; lst (* _Robert G. Wilson v_, Jun 27 2010 *)
%o (PARI) xigma(n)=local(ds,r);ds=divisors(n);for(k=1,#ds,r=bitxor(r,ds[k]));r
%o for(n=1,1000000000,if(xigma(n)==n,print1(n",")))
%Y Cf. A178910, A178909, A000396, A003987.
%K nonn,base
%O 1,2
%A _Franklin T. Adams-Watters_, Jun 22 2010
%E a(17) from _Robert G. Wilson v_, Jul 30 2010
%E a(18)-a(23) from _Donovan Johnson_, Mar 12 2011
%E a(24)-a(27) from _Giovanni Resta_, Aug 14 2019
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