A091507 Product of the anti-divisors of n.

2, 3, 6, 4, 30, 15, 12, 84, 42, 40, 270, 108, 120, 33, 2310, 1680, 78, 312, 168, 8100, 4050, 112, 7140, 204, 11880, 25080, 114, 960, 7938, 257985, 17160, 276, 19320, 192, 11250, 1732500, 24024, 11664, 1458, 114240, 14790, 696, 5896800, 33852, 17670

Offset: 3

Author

Lior Manor, Mar 03 2004

Keywords

• nonn

Comments

See A066272 for definition of anti-divisor.

Examples

			For example, n = 18: 2n-1, 2n, 2n+1 are 35, 36, 37 with odd divisors > 1 {3,7,35}, {3,9}, {37} and quotients 7, 5, 1, 12, 4, 1, so the anti-divisors of 12 are 4, 5, 7, 12. Therefore a(18) = 4*5*7*12 = 1680.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 3..1000
• Jon Perry, Anti-divisors.
• Jon Perry, The Anti-divisor [Cached copy]
• Jon Perry, The Anti-divisor: Even More Anti-Divisors [Cached copy]

Crossrefs

Cf. A066417.

Programs

Maple

A091507 := proc(n)
        mul( a, a=antidivisors(n)) ; # reuse A066272
end proc:
seq(A091507(n),n=3..10) ; # R. J. Mathar, Jan 24 2022

Mathematica

antid[n_] := Select[ Union[ Join[ Select[ Divisors[2n - 1], OddQ[ # ] && # != 1 & ], Select[ Divisors[2n + 1], OddQ[ # ] && # != 1 & ], 2n/Select[ Divisors[ 2n], OddQ[ # ] && # != 1 &]]], # < n &]; Table[ Times @@ antid[n], {n, 3, 50}] (* Robert G. Wilson v, Mar 15 2004 *)
a091507[n_Integer] := Apply[Times, Cases[Range[2, n - 1], ?(Abs[Mod[n, #] - #/2] < 1 &)]]; Array[a091507, 10000] (* _Michael De Vlieger, Aug 08 2014, after Harvey P. Dale at A066272 *)

Python

from functools import reduce
from operator import mul
def A091507(n):
    return reduce(mul,[d for d in range(2,n) if n%d and 2*n%d in [d-1,0,1]]) # Chai Wah Wu, Aug 08 2014