This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A051908 Number of ways to express 1 as the sum of unit fractions such that the sum of the denominators is n. 2
 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 3, 0, 1, 1, 1, 1, 2, 3, 2, 2, 1, 2, 2, 2, 4, 5, 5, 2, 4, 5, 5, 9, 4, 4, 6, 4, 4, 7, 8, 4, 10, 9, 9, 11, 8, 13, 13, 15, 16, 21, 18, 16, 22, 19, 18, 30, 24, 19, 26, 28, 26, 29, 35, 29, 44, 28, 47, 48, 43, 44, 59, 49, 51, 72, 65, 64, 79 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,22 COMMENTS Also the number of partitions of n whose reciprocal sums to 1; "exact partitions". [From Robert G. Wilson v, Sep 30 2009] REFERENCES Derrick Niederman, "Number Freak, From 1 to 200 The Hidden Language of Numbers Revealed", a Perigee Book, Penguin Group, NY, 2009, page 82&83. [From Robert G. Wilson v, Sep 30 2009] LINKS EXAMPLE 1 = 1/2+1/2, the sum of denominators is 4, this is the only expression of 1 as unit fractions with denominator sum 4, so a(4)=1. MATHEMATICA (* first do *) << "Combinatorica`"; (* then *) f[n_] := Block[{c = i = 0, k = PartitionsP@n, p = {n}}, While[i < k, If[1 == Plus @@ (1/p), c++ ]; i++; p = NextPartition@p]; c]; Array[f, 88] [From Robert G. Wilson v, Sep 30 2009] CROSSREFS A028229 lists n such that a(n)=0. Cf. A058360. [From Robert G. Wilson v, Sep 30 2009] Sequence in context: A065714 A110700 A181875 * A056614 A092510 A126309 Adjacent sequences:  A051905 A051906 A051907 * A051909 A051910 A051911 KEYWORD nonn AUTHOR Jud McCranie, Dec 16 1999 EXTENSIONS a(n)>0 for n>23. a(87) & a(88) from Robert G. Wilson v, Sep 30 2009 STATUS approved

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

Content is available under The OEIS End-User License Agreement .