A225817 - OEIS

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

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OFFSET

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