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%I #28 Mar 13 2018 04:07:40
%S 3,4,6,9,36,54,96,216,576,1296,69984,236196,393216,497664,28697814,
%T 31850496
%N Numbers k such that the least common multiple of the anti-divisors of k is less than k.
%C Numbers k such that lcm(anti-divisors(k)) < lcm(divisors(k)).
%C The numbers in the sequence up to a(n) = 1296 are of the form 2^x * 3^y. Checking all values of x and y between 1 and 9, there is one additional term, 69984.
%C Numbers in sequence up to a(n) = 31850496 are of the form 2^x * 3^y, x >= 0, y >= 0. Searching through x <= 40 and y <= 40, the following terms in the sequence are found: 84934656, 2038431744, 5435817984, 1174136684544, 28179280429056, 42268920643584, 75144747810816, 289207845356544, 570630428688384, 30814043149172736. - _Chai Wah Wu_, Aug 20 2014
%e a(6) = 9 because lcm(2, 6) = 6, which is less than 9.
%t antiDivisors[n_Integer] :=
%t Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)];
%t a242028[n_Integer] := Select[Range[n],
%t Length[antiDivisors[#]] > 0 && LCM @@ antiDivisors[#] < # &]; a242028[5000] (* _Michael De Vlieger_, Aug 21 2014 *)
%o (Python)
%o from sympy import divisors, lcm
%o A242028 = [n for n in range(3,10**5) if lcm(
%o ..........[2*d for d in divisors(n) if n > 2*d and n % (2*d)] +
%o ..........[d for d in divisors(2*n-1) if n > d >=2 and n % d] +
%o ..........[d for d in divisors(2*n+1) if n > d >=2 and n % d]) < n]
%o # _Chai Wah Wu_, Aug 19 2014
%Y Cf. A096357.
%K nonn,more
%O 1,1
%A _Michael De Vlieger_, suggested by _Michel Marcus_, Aug 11 2014
%E Corrected comment, removed 1 and 2 from sequence and added a(11)-a(16) by _Chai Wah Wu_, Aug 20 2014
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