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 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
CROSSREFS
KEYWORD
nonn
AUTHOR
Lior Manor, Mar 03 2004
STATUS
approved