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%I #47 Oct 15 2021 19:49:02
%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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