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 A058360 Number of partitions of n whose reciprocal sum is an integer. 33
 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; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Also the number of ways to express an integer as the sum of unit fractions such that the sum of the denominators is n. REFERENCES 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). LINKS Seiichi Manyama, Table of n, a(n) for n = 1..80 EXAMPLE 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. MATHEMATICA (* 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] CROSSREFS Cf. A066824, A051908. Sequence in context: A194815 A029080 A147652 * A241901 A238213 A193942 Adjacent sequences:  A058357 A058358 A058359 * A058361 A058362 A058363 KEYWORD nonn AUTHOR Robert G. Wilson v, Jan 25 2002, Sep 30 2009 STATUS approved

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Last modified April 4 21:43 EDT 2020. Contains 333238 sequences. (Running on oeis4.)