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A191907 Square array read by antidiagonals up: T(n,k) = -(n-1) if n divides k, else 1.

%I A191907 #14 Dec 10 2016 17:13:12
%S A191907 0,1,0,1,-1,0,1,1,1,0,1,1,-2,-1,0,1,1,1,1,1,0,1,1,1,-3,1,-1,0,1,1,1,1,
%T A191907 1,-2,1,0,1,1,1,1,-4,1,1,-1,0,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,-5,1,-3,
%U A191907 -2,-1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,-6,1,1,1,1,-1,0,1,1,1,1,1,1,1,1,1,-4,1,-2,1,0,1,1,1,1,1,1,1,-7,1,1,1,-3,1,-1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0
%N A191907 Square array read by antidiagonals up: T(n,k) = -(n-1) if n divides k, else 1.
%C A191907 Apart from the top row, the same as A177121.
%C A191907 Sum_{k>=1} T(n,k)/k = log(n); this has been pointed out by _Jaume Oliver Lafont_ in A061347 and A002162.
%F A191907 If n divides k then T(n,k) = -(n-1) else 1.
%e A191907 Table starts:
%e A191907 0..0..0..0..0..0..0..0..0...
%e A191907 1.-1..1.-1..1.-1..1.-1..1...
%e A191907 1..1.-2..1..1.-2..1..1.-2...
%e A191907 1..1..1.-3..1..1..1.-3..1...
%e A191907 1..1..1..1.-4..1..1..1..1...
%e A191907 1..1..1..1..1.-5..1..1..1...
%e A191907 1..1..1..1..1..1.-6..1..1...
%e A191907 1..1..1..1..1..1..1.-7..1...
%e A191907 1..1..1..1..1..1..1..1.-8...
%t A191907 Clear[t, n, k];
%t A191907 nn = 30;
%t A191907 t[n_, k_] := t[n, k] = If[Mod[n, k] == 0, -(k - 1), 1]
%t A191907 MatrixForm[Transpose[Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}]]]
%o A191907 (PARI) N=20; M=matrix(N,N,n,k, if(n%k==0,1-k,1))~
%Y A191907 Cf. A002162, A002391, A016627, A191904.
%K A191907 sign,tabl
%O A191907 1,13
%A A191907 _Mats Granvik_, Jun 19 2011