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A091507 Product of the anti-divisors of n. 5
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 (list; graph; refs; listen; history; text; internal format)
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

P:=proc(q) local a, k, n; for n from 3 to q do a:=1;

for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=a*k; fi; od;

print(a); od; end: P(10^3); # Paolo P. Lava, Oct 01 2013

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 xrange(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

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Last modified November 19 00:12 EST 2018. Contains 317332 sequences. (Running on oeis4.)