This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A154888 Number of ways to partition 1 into distinct reduced fractions i/j with j<=n. 4
 1, 1, 2, 3, 5, 7, 11, 16, 24, 37, 48, 71, 88, 133, 284, 435, 472, 773, 826, 1835, 4369, 5546, 5649, 9924, 16465, 19944, 32324, 75913, 76168, 140802, 141141, 238514, 537697, 598296, 2556065, 4674085, 4674844, 4985386, 9716587, 23983712, 23984971 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) = A116084(n)+1 for all n because the decompositions are the same except for the additional fraction 1/1 allowed here but excluded in A116084. - M. F. Hasler, Jul 14 2016 LINKS EXAMPLE a(6) = #[1, 5/6+1/6, 4/5+1/5, 3/4+1/4, 2/3+1/3, 3/5+2/5, 1/2+1/3+1/6] = 7. MATHEMATICA Farey[n_] := Union@ Flatten@ Table[ a/b, {b, n}, {a, b}]; t[n_, k_] := t[n, k] = Block[{c = j = 0, ip = IntegerPartitions[1, {k}, Farey@ n]}, len = 1 + Length@ ip; While[j < len, If[Plus @@ Union@ ip[[j]] == 1, c++ ]; j++ ]; c]; f[n_] := Plus @@ Table[ t[n, k], {k, Ceiling[n/2]}]; Array[f, 24] (* Robert G. Wilson v, Aug 30 2010 *) CROSSREFS Cf. A119983, A154887. Equals A116084(n) + 1. Sequence in context: A083198 A112088 A117792 * A271485 A018057 A130137 Adjacent sequences:  A154885 A154886 A154887 * A154889 A154890 A154891 KEYWORD more,nonn AUTHOR Reinhard Zumkeller, Jan 18 2009 EXTENSIONS a(22)-a(26) from Robert G. Wilson v, Aug 30 2010 a(27)-a(34) from Don Reble, Jul 13 2016 a(35)-a(41) from Giovanni Resta, Jul 15 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.