Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001293
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Mapping
St001293: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 1
[1,2] => 9
[2,1] => 8
[1,2,3] => 55
[1,3,2] => 54
[2,1,3] => 50
[2,3,1] => 47
[3,1,2] => 47
[3,2,1] => 45
[1,2,3,4] => 875
[1,2,4,3] => 870
[1,3,2,4] => 861
[1,3,4,2] => 848
[1,4,2,3] => 848
[1,4,3,2] => 840
[2,1,3,4] => 805
[2,1,4,3] => 800
[2,3,1,4] => 763
[2,3,4,1] => 736
[2,4,1,3] => 750
[2,4,3,1] => 728
[3,1,2,4] => 763
[3,1,4,2] => 750
[3,2,1,4] => 735
[3,2,4,1] => 708
[3,4,1,2] => 700
[3,4,2,1] => 686
[4,1,2,3] => 736
[4,1,3,2] => 728
[4,2,1,3] => 708
[4,2,3,1] => 686
[4,3,1,2] => 686
[4,3,2,1] => 672
[1,2,3,4,5] => 2877
[1,2,3,5,4] => 2870
[1,2,4,3,5] => 2862
[1,2,4,5,3] => 2845
[1,2,5,3,4] => 2845
[1,2,5,4,3] => 2835
[1,3,2,4,5] => 2835
[1,3,2,5,4] => 2828
[1,3,4,2,5] => 2796
[1,3,4,5,2] => 2764
[1,3,5,2,4] => 2779
[1,3,5,4,2] => 2754
[1,4,2,3,5] => 2796
[1,4,2,5,3] => 2779
[1,4,3,2,5] => 2772
[1,4,3,5,2] => 2740
[1,4,5,2,3] => 2730
Description
The sum of all $1/(i+\pi(i))$ for a permutation $\pi$ times the lcm of all possible values among permutations of the same length. It turns out that the least common multiple of all values is [1], so this statistic is given by $$ k \cdot \sum_{i=1}^n \frac{1}{i+\pi(i)}$$ where $\pi$ is a permutation of length $n$ and $k = \operatorname{lcm}\{ 1,\dots,2n\}$.