A242028 Numbers k such that the least common multiple of the anti-divisors of k is less than k.

3, 4, 6, 9, 36, 54, 96, 216, 576, 1296, 69984, 236196, 393216, 497664, 28697814, 31850496

Offset

1,1

Comments

Numbers k such that lcm(anti-divisors(k)) < lcm(divisors(k)).

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.

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

Links

Table of n, a(n) for n=1..16.

Example

a(6) = 9 because lcm(2, 6) = 6, which is less than 9.

Mathematica

antiDivisors[n_Integer] :=
  Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)];
a242028[n_Integer] := Select[Range[n],
  Length[antiDivisors[#]] > 0 && LCM @@ antiDivisors[#] < # &]; a242028[5000] (* Michael De Vlieger, Aug 21 2014 *)

Prog

(Python)
from sympy import divisors, lcm
A242028 = [n for n in range(3, 10**5) if lcm(
..........[2*d for d in divisors(n) if n > 2*d and n % (2*d)] +
..........[d for d in divisors(2*n-1) if n > d >=2 and n % d] +
..........[d for d in divisors(2*n+1) if n > d >=2 and n % d]) < n]
# Chai Wah Wu, Aug 19 2014

Crossrefs

Cf. A096357.

Sequence in context: A191699 A293272 A192286 * A254002 A095729 A185739

Adjacent sequences: A242025 A242026 A242027 * A242029 A242030 A242031

Keyword

nonn,more

Author

Michael De Vlieger, suggested by Michel Marcus, Aug 11 2014

Extensions

Corrected comment, removed 1 and 2 from sequence and added a(11)-a(16) by Chai Wah Wu, Aug 20 2014

Status

approved