A225817 Moebius function applied to divisors of n, table read by rows.

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, -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, 0, 0, 1, -1, 1, -1, 0, -1, 1, 0, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1

Offset

1

Comments

T(n,k) = A008683(A027750(n,k)), k = 1..A000005(n);

T(n,1) = 1; for n > 1: T(n,2) = -1;

T(n,A000005(n)) = A008683(n);

A048105(n) = number of zeros in row n;

A034444(n) = number of nonzero terms in row n;

A007875(n) = number of ones in row n.

Links

Reinhard Zumkeller, Rows n = 1..1000 of table, flattened

Example

.   n  |  Initial rows                     |   A027750(n,[1..A000005(n)])
. -----+-----------------------------------+-- divisors of n: -----------
.   1  |  1                                |   1
.   2  |  1  -1                            |   1,2
.   3  |  1  -1                            |   1,3
.   4  |  1  -1  0                         |   1,2,4
.   5  |  1  -1                            |   1,5
.   6  |  1  -1  -1   1                    |   1,2,3,6
.   7  |  1  -1                            |   1,7
.   8  |  1  -1   0   0                    |   1,2,4,8
.   9  |  1  -1   0                        |   1,3,9
.  10  |  1  -1  -1   1                    |   1,2,5,10
.  11  |  1  -1                            |   1,11
.  12  |  1  -1  -1   0   1   0            |   1,2,3,4,6,12
.  13  |  1  -1                            |   1,13
.  14  |  1  -1  -1   1                    |   1,2,7,14
.  15  |  1  -1  -1   1                    |   1,3,5,15
.  16  |  1  -1   0   0   0                |   1,2,4,8,16
.  17  |  1  -1                            |   1,17
.  18  |  1  -1  -1   1   0   0            |   1,2,3,6,9,18
.  19  |  1  -1                            |   1,19
.  20  |  1  -1   0  -1   1   0            |   1,2,4,5,10,20
.  21  |  1  -1  -1   1                    |   1,3,7,21
.  22  |  1  -1  -1   1                    |   1,2,11,22
.  23  |  1  -1                            |   1,23
.  24  |  1  -1  -1   0   1   0   0   0    |   1,2,3,4,6,8,12,24
.  25  |  1  -1   0                        |   1,5,25
.  26  |  1  -1  -1   1                    |   1,2,13,26
.  27  |  1  -1   0   0                    |   1,3,9,27
.  28  |  1  -1   0  -1   1   0            |   1,2,4,7,14,28
.  29  |  1  -1                            |   1,29
.  30  |  1  -1  -1  -1   1   1   1  -1    |   1,2,3,5,6,10,15,30 .

Mathematica

Table[Map[MoebiusMu, Divisors[n]], {n, 1, 20}] // Grid (* Geoffrey Critzer, Dec 10 2014 *)

Prog

(Haskell)
a225817 n k = a225817_tabf !! (n-1) !! (k-1)
a225817_row n = a225817_tabf !! (n-1)
a225817_tabf = map (map a008683) a027750_tabf

Crossrefs

Cf. A000005 (row lengths), A063524 (row sums), A069158 (row products).

Sequence in context: A071025 A077010 A330548 * A355823 A355825 A332732

Adjacent sequences: A225814 A225815 A225816 * A225818 A225819 A225820

Keyword

sign,tabf

Author

Reinhard Zumkeller, Jul 30 2013

Status

approved