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A066824 Sum of the reciprocals of the partitions of n enumerated in A058360. 1
1, 2, 3, 5, 7, 9, 11, 15, 19, 24, 30, 39, 48, 58, 69, 84, 100, 120, 142, 171, 200, 237, 275, 323, 372, 437, 505, 589, 678, 787, 904, 1042, 1189, 1365, 1557, 1785, 2031, 2327, 2638, 3009, 3405, 3875, 4376, 4970, 5610, 6356, 7166, 8081, 9082, 10225, 11469 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..51.

EXAMPLE

a(12) = 39 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 which together equals 39.

MATHEMATICA

<< DiscreteMath`Combinatorica`; f[n_] := (p = Partitions[n]; is = Compile[ {{x, _Integer, 1}}, Plus @@ (1/x)]; ans = p[[ Flatten[ Position[ FractionalPart[ is /@ p], x_ /; x < .000001 || x > 0.999999]]]]); g[n_] := (q = f[n]; s = 0; k = 1; l = Length[q]; While[k < l + 1, s = s + is[ q[[k]]]; k++ ]; IntegerPart[s]); Table[ Length[ f[n]], {n, 1, 65} ]

CROSSREFS

Sequence in context: A323648 A238526 A281541 * A036963 A120431 A214548

Adjacent sequences:  A066821 A066822 A066823 * A066825 A066826 A066827

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jan 25 2002

STATUS

approved

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Last modified June 21 19:59 EDT 2021. Contains 345365 sequences. (Running on oeis4.)