A186287 a(n) is the denominator of the rational number whose "factorization" into terms of A186285 has the balanced ternary representation corresponding to n.

1, 1, 2, 1, 1, 6, 3, 3, 2, 1, 1, 2, 1, 1, 30, 15, 15, 10, 5, 5, 10, 5, 5, 6, 3, 3, 2, 1, 1, 2, 1, 1, 6, 3, 3, 2, 1, 1, 2, 1, 1, 105, 105, 105, 35, 35, 35, 35, 35, 35, 21, 21, 21, 7, 7, 7, 7, 7, 7, 21, 21, 21, 7, 7, 7, 7, 7, 7, 15, 15, 15, 5, 5, 5, 5, 5, 5, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 3

Offset: 0

Author

Daniel Forgues, Feb 17 2011

Keywords

• nonn
• frac

Comments

Denominators from the ordering of positive rational numbers by increasing balanced ternary representation of the "factorization" of positive rational numbers into terms of A186285 (prime powers with a power of three as exponent).

Examples

			The balanced ternary digits {-1,0,+1} are represented here as {2,0,1}.
   n BalTern A186286/A186287 (in reduced form)
   0      0  Empty product = 1 = 1/1, a(n) = 1
   1      1  2 = 2/1,                 a(n) = 1
   2     12  3*(1/2) = 3/2,           a(n) = 2
   3     10  3 = 3/1,                 a(n) = 1
   4     11  3*2 = 6 = 6/1,           a(n) = 1
   5    122  5*(1/3)*(1/2) = 5/6,     a(n) = 6
   6    120  5*(1/3) = 5/3,           a(n) = 3
   7    121  5*(1/3)*2 = 10/3,        a(n) = 3
...    ...
  41  12222  8*(1/7)*(1/5)*(1/3)*(1/2) = 8/210 = 4/105, a(n) = 105
		

Links

• Daniel Forgues, Table of n, a(n) for n = 0..9841
• OEIS Wiki, Orderings of rational numbers

Crossrefs

Cf. A186285, A186286, A185169, A052330.

Formula

The balanced ternary representation of n

n = Sum(i=0..1+floor(log_3(2|n|)) n_i * 3^i, n_i in {-1,0,1},

is taken as the representation of the "factorization" of the positive rational number c(n)/d(n) into terms from A186285

c(n)/d(n) = Prod(i=0..1+floor(log_3(2|n|)) (A186285(i+1))^(n_i), where A186285(i+1) is the (i+1)th prime power with exponent being a power of 3. Then a(n) is the denominator, i.e., d(n).