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A189043 For all permutations of [1..n]: number of distinct values taken by sum(k=1..n, k^2 * pi(k) ). 0

%I

%S 1,2,6,23,89,232,437,747,1191,1806,2631,3709,5087,6816

%N For all permutations of [1..n]: number of distinct values taken by sum(k=1..n, k^2 * pi(k) ).

%e The permutations of 4 elements and the respective sums are

%e [ 1 2 3 4 ] 100

%e [ 1 2 4 3 ] 93

%e [ 1 3 2 4 ] 95

%e [ 1 3 4 2 ] 81

%e [ 1 4 2 3 ] 83

%e [ 1 4 3 2 ] 76

%e [ 2 1 3 4 ] 97

%e [ 2 1 4 3 ] 90

%e [ 2 3 1 4 ] 87

%e [ 2 3 4 1 ] 66

%e [ 2 4 1 3 ] 75

%e [ 2 4 3 1 ] 61

%e [ 3 1 2 4 ] 89

%e [ 3 1 4 2 ] 75 // same as [ 2 4 1 3 ]

%e [ 3 2 1 4 ] 84

%e [ 3 2 4 1 ] 63

%e [ 3 4 1 2 ] 60

%e [ 3 4 2 1 ] 53

%e [ 4 1 2 3 ] 74

%e [ 4 1 3 2 ] 67

%e [ 4 2 1 3 ] 69

%e [ 4 2 3 1 ] 55

%e [ 4 3 1 2 ] 57

%e [ 4 3 2 1 ] 50

%e All values except 75 are unique, so a(4) = 4!-1 = 23.

%Y Cf. A126972 (sum k*pi(k)).

%K nonn,more

%O 1,2

%A _Joerg Arndt_, Apr 22 2011

%E Corrected terms (error pointed out by _Alois P. Heinz_), _Joerg Arndt_, Apr 28 2011.

%E a(14) from _Alois P. Heinz_, Apr 28 2011

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Last modified September 30 00:37 EDT 2020. Contains 337432 sequences. (Running on oeis4.)