A066481 Largest anti-divisor of n.

2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 43, 43, 44, 45, 45, 46, 47, 47, 48, 49, 49, 50

Offset: 3

Author

Robert G. Wilson v, Jan 02 2002

Keywords

• nonn

Comments

Apart from initial terms this is identical to A004396.

See A066272 for definition of anti-divisor.

Links

• Seiichi Manyama, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A066482.

Programs

Maple

antidivisors := proc(n)
   local a, k;
   a := {} ;
   for k from 2 to n-1 do
      if abs((n mod k)- k/2) < 1 then
         a := a union {k} ;
      end if;
   end do:
   a ;
end proc:
A066481 := proc(n)
if n < 3 then
    return 0;
else
    sort(convert(antidivisors(n),list)) ;
    op(-1,%) ;
end if;
end proc: # R. J. Mathar, Mar 15 2013

Mathematica

antid[n_] := Select[ Union[ Join[ Select[ Divisors[2n - 1], OddQ[ # ] && # != 1 &], Select[ Divisors[2n + 1], OddQ[ # ] && # != 1 &], 2n/Select[ Divisors[2*n], OddQ[ # ] && # != 1 &]]], # < n & ]; Table[ Last[ antid[n]], {n, 3, 100} ]

PARI

a(n)=2*n\/3 \\ Charles R Greathouse IV, Feb 27 2013