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

3,1

Comments

See A066272 for definition of anti-divisor.

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]

Example

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.

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 *)

Prog

(Python)
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

Crossrefs

Cf. A066417.

Sequence in context: A282507 A156055 A096357 * A098282 A034855 A105214

Adjacent sequences: A091504 A091505 A091506 * A091508 A091509 A091510

Keyword

nonn

Author

Lior Manor, Mar 03 2004

Status

approved