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A191910 Triangle read by rows: T(n,n)=n; T(n,k) = k-1 if k divides n and k < n, otherwise -1.

%I A191910 #23 Mar 05 2019 01:43:54
%S A191910 1,0,2,0,-1,3,0,1,-1,4,0,-1,-1,-1,5,0,1,2,-1,-1,6,0,-1,-1,-1,-1,-1,7,
%T A191910 0,1,-1,3,-1,-1,-1,8,0,-1,2,-1,-1,-1,-1,-1,9,0,1,-1,-1,4,-1,-1,-1,-1,
%U A191910 10,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,11,0,1,2,3,-1,5,-1,-1,-1,-1,-1,12,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,13
%N A191910 Triangle read by rows: T(n,n)=n; T(n,k) = k-1 if k divides n and k < n, otherwise -1.
%C A191910 The double limit lim_{k->infinity} (lim_{m->infinity} (Sum_{n=1..m} T(n,k)/n)) equals the Euler-Mascheroni constant A001620.
%e A191910 Triangle starts:
%e A191910   1;
%e A191910   0,  2;
%e A191910   0, -1,  3;
%e A191910   0,  1, -1,  4;
%e A191910   0, -1, -1, -1,  5;
%e A191910   0,  1,  2, -1, -1,  6;
%e A191910   0, -1, -1, -1, -1, -1,  7;
%e A191910   0,  1, -1,  3, -1, -1, -1,  8;
%e A191910   0, -1,  2, -1, -1, -1, -1, -1,  9;
%p A191910 A191910 := proc(n,k) if n = k then n; elif modp(n,k) = 0 then k-1 ; else -1; end if; end proc: seq(seq(A191910(n,k),k=1..n),n=1..20); # _R. J. Mathar_, Aug 03 2011
%t A191910 Clear[t];
%t A191910 nn = 13;
%t A191910 t[n_, k_] :=
%t A191910   t[n, k] = If[n <= k, 1, 0] - If[Mod[n, k] == 0, (1 - k), 1];
%t A191910 Flatten[Table[Table[t[n, k], {k, 1, n}], {n, 1, nn}]]
%t A191910 (*The double limit for gamma:*)
%t A191910 Clear[t];
%t A191910 nn = 1000;
%t A191910 kk = 60;
%t A191910 t[n_, k_] :=
%t A191910   t[n, k] = If[n <= k, 1, 0] - If[Mod[n, k] == 0, (1 - k), 1];
%t A191910 a = Table[t[n, kk], {n, 1, nn}];
%t A191910 MatrixForm[a];
%t A191910 b = Range[nn];
%t A191910 gamma = N[Total[a/b]]
%Y A191910 Cf. A001620, A191907.
%K A191910 sign,tabl,easy
%O A191910 1,3
%A A191910 _Mats Granvik_, Jun 19 2011