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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.
2
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, 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, 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
OFFSET
1,3
COMMENTS
The double limit lim_{k->infinity} (lim_{m->infinity} (Sum_{n=1..m} T(n,k)/n)) equals the Euler-Mascheroni constant A001620.
EXAMPLE
Triangle starts:
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;
0, 1, -1, 3, -1, -1, -1, 8;
0, -1, 2, -1, -1, -1, -1, -1, 9;
MAPLE
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
MATHEMATICA
Clear[t];
nn = 13;
t[n_, k_] :=
t[n, k] = If[n <= k, 1, 0] - If[Mod[n, k] == 0, (1 - k), 1];
Flatten[Table[Table[t[n, k], {k, 1, n}], {n, 1, nn}]]
(*The double limit for gamma:*)
Clear[t];
nn = 1000;
kk = 60;
t[n_, k_] :=
t[n, k] = If[n <= k, 1, 0] - If[Mod[n, k] == 0, (1 - k), 1];
a = Table[t[n, kk], {n, 1, nn}];
MatrixForm[a];
b = Range[nn];
gamma = N[Total[a/b]]
CROSSREFS
Sequence in context: A141097 A278045 A096335 * A129503 A225682 A144185
KEYWORD
sign,tabl,easy
AUTHOR
Mats Granvik, Jun 19 2011
STATUS
approved