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Search: id:A058360
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| A058360 |
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Number of partitions of n whose reciprocal sum is an integer. |
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+0
3
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| 1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 19, 23, 25, 31, 33, 38, 42, 51, 57, 66, 75, 86, 97, 109, 122, 138, 155, 177, 200, 230, 253, 287, 320, 363, 405, 456, 507, 572, 639, 707, 785, 877, 971, 1079, 1198, 1334, 1476, 1635, 1802, 2002, 2213, 2445, 2700
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Also the number of ways to express an integer as the sum of unit fractions such that the sum of the denominators is n.
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REFERENCES
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From a question posted to the news group comp.soft-sys.math.mathematica by "Juan" (erfa11(AT)hotmail.com) at Steven M. Christensen and Associates, Inc. and MathTensor, Inc. Jan 22, 2002 08:46:57 +0000 (UTC).
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EXAMPLE
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a(12) = 7 because the partitions of 12 whose reciprocal sum is an integer are: {{6, 3, 2, 1}, {4, 4, 2, 1, 1}, {3, 3, 3, 1, 1, 1}, {2, 2, 2, 2, 2, 2}, {2, 2, 2, 2, 1, 1, 1, 1}, {2, 2, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}}. Individually their reciprocal sums are: 2, 3, 4, 3, 6, 9 and 12.
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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[ IntegerQ[ Plus @@ (1/p)], c++ ]; i++; p = NextPartition@ p]; c]; Array[f, 61]
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CROSSREFS
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Cf. A066824, A051908.
Sequence in context: A029101 A029080 A147652 this_sequence A098527 A035635 A029100
Adjacent sequences: A058357 A058358 A058359 this_sequence A058361 A058362 A058363
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 25 2002, Sep 30 2009
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