|
|
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
|
|
|
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
|
mul( a, a=antidivisors(n)) ; # reuse A066272
end proc:
|
|
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 *)
|
|
PROG
|
(Python)
from operator import mul
....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
|
|
|
STATUS
|
approved
|
|
|
|