A178911 Perfex numbers: n = binary XOR of divisors of n.

1, 6, 120, 198, 3696, 6240, 32640, 56160, 1941408, 3592200, 8119800, 15628032, 27125280, 59032080, 61788240, 125859840, 1635834720, 2147450880, 3709081680, 16328199552, 26198072160, 52344970080, 52396088160, 209584184160, 210197601120, 236223190200, 237385437360

Offset: 1

Author

Franklin T. Adams-Watters, Jun 22 2010

Keywords

• nonn
• base

Comments

a(17) > 1e9.

10^11 < a(24) <= 209584184160. a(25) <= 210197601120. - Donovan Johnson, Mar 12 2011

a(28) > 3*10^11. - Giovanni Resta, Aug 14 2019

Crossrefs

Cf. A178910, A178909, A000396, A003987.

Programs

Mathematica

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 *)

PARI

xigma(n)=local(ds,r);ds=divisors(n);for(k=1,#ds,r=bitxor(r,ds[k]));r
for(n=1,1000000000,if(xigma(n)==n,print1(n",")))

Extensions

a(17) from Robert G. Wilson v, Jul 30 2010

a(18)-a(23) from Donovan Johnson, Mar 12 2011

a(24)-a(27) from Giovanni Resta, Aug 14 2019