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

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

Offset: 1

Author

Joerg Arndt, Apr 22 2011

Keywords

• nonn
• more

Examples

			The permutations of 4 elements and the respective sums are
[ 1 2 3 4 ] 100
[ 1 2 4 3 ]  93
[ 1 3 2 4 ]  95
[ 1 3 4 2 ]  81
[ 1 4 2 3 ]  83
[ 1 4 3 2 ]  76
[ 2 1 3 4 ]  97
[ 2 1 4 3 ]  90
[ 2 3 1 4 ]  87
[ 2 3 4 1 ]  66
[ 2 4 1 3 ]  75
[ 2 4 3 1 ]  61
[ 3 1 2 4 ]  89
[ 3 1 4 2 ]  75  // same as [ 2 4 1 3 ]
[ 3 2 1 4 ]  84
[ 3 2 4 1 ]  63
[ 3 4 1 2 ]  60
[ 3 4 2 1 ]  53
[ 4 1 2 3 ]  74
[ 4 1 3 2 ]  67
[ 4 2 1 3 ]  69
[ 4 2 3 1 ]  55
[ 4 3 1 2 ]  57
[ 4 3 2 1 ]  50
All values except 75 are unique, so a(4) = 4!-1 = 23.
		

Crossrefs

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

Extensions

Corrected terms (error pointed out by Alois P. Heinz), Joerg Arndt, Apr 28 2011.

a(14) from Alois P. Heinz, Apr 28 2011