A066824 Sum of the reciprocals of the partitions of n enumerated in A058360.

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

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: A353037 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