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 A143256 Triangle read by rows, matrix multiplication A051731 * A128407 * A127648, 1<=k<=n. 3
 1, 1, -2, 1, 0, -3, 1, -2, 0, 0, 1, 0, 0, 0, -5, 1, -2, -3, 0, 0, 6, 1, 0, 0, 0, 0, 0, -7, 1, -2, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, -5, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 1, -2, -3, 0, 0, 6, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 1, -2, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 14 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Right border = n*mu(n) = A055615. Row sums = A023900: (1, -1, -2, -1, -4, 2, -6,...). LINKS Robert Israel, Table of n, a(n) for n = 1..9870 FORMULA Triangle read by rows, A051731 * A128407 * A127648, 1<=k<=n EXAMPLE First few rows of the triangle = 1; 1, -2; 1, 0, -3; 1, -2, 0, 0; 1, 0, 0, 0, -5; 1, -2, -3, 0, 0, 6; 1, 0, 0, 0, 0, 0, -7; ... MAPLE seq(seq(`if`(i mod j = 0, j*numtheory:-mobius(j), 0), j=1..i), i=1..20); # Robert Israel, Sep 07 2014 MATHEMATICA Table[If[Divisible[n, k], k MoebiusMu[k], 0], {n, 1, 14}, {k, 1, n}] (* Jean-François Alcover, Jun 19 2019 *) PROG (Sage) A143256_row = lambda n: [k*moebius(k) if k.divides(n) else 0 for k in (1..n)] for n in (1..10): print(A143256_row(n)) # Peter Luschny, Jan 05 2018 CROSSREFS Cf. A008683, A055615, A051731, A128407, A127648, A023900. Sequence in context: A287352 A243715 A333661 * A143151 A130106 A127093 Adjacent sequences:  A143253 A143254 A143255 * A143257 A143258 A143259 KEYWORD tabl,sign AUTHOR Gary W. Adamson, Aug 02 2008 STATUS approved

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Last modified April 14 07:32 EDT 2021. Contains 342946 sequences. (Running on oeis4.)