login
A178911
Perfex numbers: n = binary XOR of divisors of n.
2
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
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
KEYWORD
nonn,base
AUTHOR
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