A154886 Number of ways to partition n into reduced fractions i/j with j <= n.
1, 5, 51, 655, 20980, 578779, 46097340, 2889706132, 485416306983, 68334145684271, 24330218582223815, 3847311627258606534, 2716890193805515507433, 1270766589764097820833691, 2188031110546839992589840986, 1331298554328475793875243619997
Offset: 1
Keywords
Examples
a(2) = #{2, 3/2+1/2, 1+1, 1+1/2+1/2, 1/2+1/2+1/2+1/2} = 5.
Links
- Robert Gerbicz, Table of n, a(n) for n = 1..43
Programs
-
Mathematica
modifiedFarey[n_] := Union@ Flatten@ Table[a/b, {b, n}, {a, b*n}]; t[n_, k_] := Length@ IntegerPartitions[n, {k}, modifiedFarey@ n]; Plus @@@ Table[t[n, k], {n, 7, 7}, {k, n*(Plus @@ EulerPhi@ Range@n)}] (* Robert G. Wilson v, Aug 30 2010 *)
Extensions
a(7) from Robert G. Wilson v, Aug 30 2010
a(8)-a(16) from Robert Gerbicz, Nov 19 2010