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

1,2

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

Links

Table of n, a(n) for n=1..27.

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 *)

Prog

(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", ")))

Crossrefs

Cf. A178910, A178909, A000396, A003987.

Sequence in context: A246827 A127726 A117063 * A227027 A001219 A224303

Adjacent sequences: A178908 A178909 A178910 * A178912 A178913 A178914

Keyword

nonn,base

Author

Franklin T. Adams-Watters, Jun 22 2010

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

Status

approved