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
Keywords
Examples
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.
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).
Programs
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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} ]