A143256 - OEIS

%I #13 Jun 19 2019 10:04:33

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

%C Right border = n*mu(n) = A055615.

%C Row sums = A023900: (1, -1, -2, -1, -4, 2, -6,...).

%H Robert Israel, <a href="/A143256/b143256.txt">Table of n, a(n) for n = 1..9870</a>

%F Triangle read by rows, A051731 * A128407 * A127648, 1<=k<=n

%e First few rows of the triangle =

%e 1;

%e 1, -2;

%e 1, 0, -3;

%e 1, -2, 0, 0;

%e 1, 0, 0, 0, -5;

%e 1, -2, -3, 0, 0, 6;

%e 1, 0, 0, 0, 0, 0, -7;

%e ...

%p seq(seq(`if`(i mod j = 0, j*numtheory:-mobius(j),0), j=1..i),i=1..20); # _Robert Israel_, Sep 07 2014

%t Table[If[Divisible[n, k], k MoebiusMu[k], 0], {n, 1, 14}, {k, 1, n}] (* _Jean-François Alcover_, Jun 19 2019 *)

%o (Sage)

%o A143256_row = lambda n: [k*moebius(k) if k.divides(n) else 0 for k in (1..n)]

%o for n in (1..10): print(A143256_row(n)) # _Peter Luschny_, Jan 05 2018

%Y Cf. A008683, A055615, A051731, A128407, A127648, A023900.

%K tabl,sign

%O 1,3

%A _Gary W. Adamson_, Aug 02 2008