ScaledReciprocalPositionValueSum on Permutation

The sum of 1/(i + p(i)) times the least common multiple of 1 .. 2n, an integer.

On Permutation

Each term is an integer, since i + p(i) is at most 2n and divides the scale (St001293).

Called as CombinatorialStat(x, "ScaledReciprocalPositionValueSum"). The head's page has its examples.

Live

Distribution

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Sizes 1 to

FindStat St001293

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.

Object	Value
[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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001293 has the rest.