%I #9 Dec 10 2014 19:31:13
%S 1,1,-1,1,-1,1,-1,0,1,-1,1,-1,-1,1,1,-1,1,-1,0,0,1,-1,0,1,-1,-1,1,1,
%T -1,1,-1,-1,0,1,0,1,-1,1,-1,-1,1,1,-1,-1,1,1,-1,0,0,0,1,-1,1,-1,-1,1,
%U 0,0,1,-1,1,-1,0,-1,1,0,1,-1,-1,1,1,-1,-1,1,1,-1
%N Moebius function applied to divisors of n, table read by rows.
%C T(n,k) = A008683(A027750(n,k)), k = 1..A000005(n);
%C T(n,1) = 1; for n > 1: T(n,2) = -1;
%C T(n,A000005(n)) = A008683(n);
%C A048105(n) = number of zeros in row n;
%C A034444(n) = number of nonzero terms in row n;
%C A007875(n) = number of ones in row n.
%H Reinhard Zumkeller, <a href="/A225817/b225817.txt">Rows n = 1..1000 of table, flattened</a>
%e . n | Initial rows | A027750(n,[1..A000005(n)])
%e . -----+-----------------------------------+-- divisors of n: -----------
%e . 1 | 1 | 1
%e . 2 | 1 -1 | 1,2
%e . 3 | 1 -1 | 1,3
%e . 4 | 1 -1 0 | 1,2,4
%e . 5 | 1 -1 | 1,5
%e . 6 | 1 -1 -1 1 | 1,2,3,6
%e . 7 | 1 -1 | 1,7
%e . 8 | 1 -1 0 0 | 1,2,4,8
%e . 9 | 1 -1 0 | 1,3,9
%e . 10 | 1 -1 -1 1 | 1,2,5,10
%e . 11 | 1 -1 | 1,11
%e . 12 | 1 -1 -1 0 1 0 | 1,2,3,4,6,12
%e . 13 | 1 -1 | 1,13
%e . 14 | 1 -1 -1 1 | 1,2,7,14
%e . 15 | 1 -1 -1 1 | 1,3,5,15
%e . 16 | 1 -1 0 0 0 | 1,2,4,8,16
%e . 17 | 1 -1 | 1,17
%e . 18 | 1 -1 -1 1 0 0 | 1,2,3,6,9,18
%e . 19 | 1 -1 | 1,19
%e . 20 | 1 -1 0 -1 1 0 | 1,2,4,5,10,20
%e . 21 | 1 -1 -1 1 | 1,3,7,21
%e . 22 | 1 -1 -1 1 | 1,2,11,22
%e . 23 | 1 -1 | 1,23
%e . 24 | 1 -1 -1 0 1 0 0 0 | 1,2,3,4,6,8,12,24
%e . 25 | 1 -1 0 | 1,5,25
%e . 26 | 1 -1 -1 1 | 1,2,13,26
%e . 27 | 1 -1 0 0 | 1,3,9,27
%e . 28 | 1 -1 0 -1 1 0 | 1,2,4,7,14,28
%e . 29 | 1 -1 | 1,29
%e . 30 | 1 -1 -1 -1 1 1 1 -1 | 1,2,3,5,6,10,15,30 .
%t Table[Map[MoebiusMu, Divisors[n]], {n, 1, 20}] // Grid (* _Geoffrey Critzer_, Dec 10 2014 *)
%o (Haskell)
%o a225817 n k = a225817_tabf !! (n-1) !! (k-1)
%o a225817_row n = a225817_tabf !! (n-1)
%o a225817_tabf = map (map a008683) a027750_tabf
%Y Cf. A000005 (row lengths), A063524 (row sums), A069158 (row products).
%K sign,tabf
%O 1
%A _Reinhard Zumkeller_, Jul 30 2013