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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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..91.

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

Cf. A001620, A191907.

Sequence in context: A141097 A278045 A096335 * A129503 A225682 A144185

Adjacent sequences:  A191907 A191908 A191909 * A191911 A191912 A191913

KEYWORD

sign,tabl,easy

AUTHOR

Mats Granvik, Jun 19 2011

STATUS

approved

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Last modified July 17 16:58 EDT 2019. Contains 325107 sequences. (Running on oeis4.)