A141673 Triangle T(n,m) read by rows: T(n,1) = n; T(n,m) = A008683(n)*n/m if m is a divisor of n, where m = 2..n, otherwise T(n,m) = 0.

1, 2, -1, 3, 0, -1, 4, 0, 0, 0, 5, 0, 0, 0, -1, 6, 3, 2, 0, 0, 1, 7, 0, 0, 0, 0, 0, -1, 8, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 10, 5, 0, 0, 2, 0, 0, 0, 0, 1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1

Offset

1,2

Comments

The function here is Mats Granvik's idea: my effort is coding it and entering it in the OEIS. All of it is based on Gary W. Adamson's A126988.

Links

G. C. Greubel, Rows n=1..100 of triangle, flattened

Example

Triangle begins
  { 1},
  { 2, -1},
  { 3,  0, -1},
  { 4,  0,  0,  0},
  { 5,  0,  0,  0, -1},
  { 6,  3,  2,  0,  0,  1},
  { 7,  0,  0,  0,  0,  0, -1},
  { 8,  0,  0,  0,  0,  0,  0,  0},
  { 9,  0,  0,  0,  0,  0,  0,  0,  0},
  {10,  5,  0,  0,  2,  0,  0,  0,  0,  1}

Mathematica

t[n_, m_] = If[m == 1, n, If[Mod[n, m] == 0, MoebiusMu[n]*n/m, 0]]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]

Prog

(PARI) T(n, m) = if (m==1, n, if (n % m, 0, moebius(n)*n/m));
tabl(nn) = for (n=1, nn, for (m=1, n, print1(T(n, m), ", ")); print); \\ Michel Marcus, Jun 10 2018

Crossrefs

Cf. A008683, A055615, A126988.

Sequence in context: A333429 A071490 A194893 * A127094 A221642 A158906

Adjacent sequences: A141670 A141671 A141672 * A141674 A141675 A141676

Keyword

sign,tabl,easy

Author

Roger L. Bagula, Gary W. Adamson and Mats Granvik, Sep 06 2008

Status

approved