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A143256 Triangle read by rows, matrix multiplication A051731 * A128407 * A127648, 1<=k<=n.

%I A143256 #13 Jun 19 2019 10:04:33
%S A143256 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,
%T A143256 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,
%U A143256 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
%N A143256 Triangle read by rows, matrix multiplication A051731 * A128407 * A127648, 1<=k<=n.
%C A143256 Right border = n*mu(n) = A055615.
%C A143256 Row sums = A023900: (1, -1, -2, -1, -4, 2, -6,...).
%H A143256 Robert Israel, <a href="/A143256/b143256.txt">Table of n, a(n) for n = 1..9870</a>
%F A143256 Triangle read by rows, A051731 * A128407 * A127648, 1<=k<=n
%e A143256 First few rows of the triangle =
%e A143256 1;
%e A143256 1, -2;
%e A143256 1, 0, -3;
%e A143256 1, -2, 0, 0;
%e A143256 1, 0, 0, 0, -5;
%e A143256 1, -2, -3, 0, 0, 6;
%e A143256 1, 0, 0, 0, 0, 0, -7;
%e A143256 ...
%p A143256 seq(seq(`if`(i mod j = 0, j*numtheory:-mobius(j),0), j=1..i),i=1..20); # _Robert Israel_, Sep 07 2014
%t A143256 Table[If[Divisible[n, k], k MoebiusMu[k], 0], {n, 1, 14}, {k, 1, n}] (* _Jean-François Alcover_, Jun 19 2019 *)
%o A143256 (Sage)
%o A143256 A143256_row = lambda n: [k*moebius(k) if k.divides(n) else 0 for k in (1..n)]
%o A143256 for n in (1..10): print(A143256_row(n)) # _Peter Luschny_, Jan 05 2018
%Y A143256 Cf. A008683, A055615, A051731, A128407, A127648, A023900.
%K A143256 tabl,sign
%O A143256 1,3
%A A143256 _Gary W. Adamson_, Aug 02 2008