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A143728 Triangle read by rows: termwise product of mu(n) and n-th row of A127368. 1
1, 1, 0, 1, -2, 0, 1, 0, -3, 0, 1, -2, -3, 0, 0, 1, 0, 0, 0, -5, 0, 1, -2, -3, 0, -5, 6, 0, 1, 0, -3, 0, -5, 0, -7, 0, 1, -2, 0, 0, -5, 0, -7, 0, 0, 1, 0, -3, 0, 0, 0, -7, 0, 0, 0, 1, -2, -3, 0, -5, 6, -7, 0, 0, 10, 1, 0, 0, 0, -5, 0, -7, 0, 0, 0, -11, 0, 1, -2, -3, 0, -5, 6, -7, 0, 0, 10, -11, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The operation A127368 * A128407 forms the termwise product of mu(n) and the n-th row of A127368: deleting all squares and changing the sign of primes to (-1).

Row sums = A143729: (1, 1, -1, -2, -4, -4, -3, -14,...)

LINKS

Table of n, a(n) for n=1..90.

FORMULA

Triangle read by rows, A127368 * A128407, 1<=k<=n; T(n,k) = {1<=k<=n, GCD(k,n)=1} * mu(k).

EXAMPLE

First few terms of the triangle = 1; 1, 0; 1, -2, 0; 1, 0, -3, 0; 1, -2, -3, 0, 0; 1, 0, 0, 0, -5, 0; 1, -2, -3, 0, -5, 6, 0; 1, 0, -3, 0, -5, 0, -7, 0; ... Example: row 7 = (1, -2, -3, 0, -5, 6, 0). We take row 7 of triangle A127368 which records the relative primes of 7 as: (1, 2, 3, 4, 5, 6, 0). Applying the termwise product of the first 7 terms of mu(k): (1, -1, -1, 0, -1, 1, -1), we get (1, -2, -3, 0, -5, 6, 0), noting that the "4" has been deleted.

CROSSREFS

Cf. A127368, A128407, A008683.

Sequence in context: A175267 A108045 A298972 * A127368 A112552 A048154

Adjacent sequences:  A143725 A143726 A143727 * A143729 A143730 A143731

KEYWORD

tabl,sign

AUTHOR

Gary W. Adamson, Aug 30 2008

EXTENSIONS

Partially edited by N. J. A. Sloane, Jan 05 2009

STATUS

approved

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Last modified March 8 00:38 EST 2021. Contains 341934 sequences. (Running on oeis4.)