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A051908
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Number of ways to express 1 as the sum of unit fractions such that the sum of the denominators is n.
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2
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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
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OFFSET
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1,22
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COMMENTS
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Also the number of partitions of n whose reciprocal sums to 1; "exact partitions". [From Robert G. Wilson v, Sep 30 2009]
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REFERENCES
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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]
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LINKS
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Table of n, a(n) for n=1..88.
Index entries for sequences related to Egyptian fractions
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EXAMPLE
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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.
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MATHEMATICA
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(* 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]
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Jud McCranie, Dec 16 1999
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EXTENSIONS
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a(n)>0 for n>23.
a(87) & a(88) from Robert G. Wilson v, Sep 30 2009
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STATUS
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approved
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