A141672 Triangle defined by T(n, k) = (n/k)*MoebiusMu(n) if n mod k is zero and T(n, 0) = n+1, read by rows.

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

Offset

0,2

Comments

Row sums are: {1, 3, 0, 0, 5, 0, 19, 0, 9, 10, 29, ...}.

Apparently this is different from A141671. - N. J. A. Sloane, Sep 13 2008

Links

G. C. Greubel, Table of n, a(n) for n = 0..5150

Formula

T(n, m) = MoebiusMu(n)*(n/m) if n mod m is zero and T(n, 0) = n+1.

Example

Triangle begins as:
   1;
   2,  1;
   3, -2, -1;
   4, -3,  0, -1;
   5,  0,  0,  0, 0;
   6, -5,  0,  0, 0, -1;
   7,  6,  3,  2, 0,  0, 1;
   8, -7,  0,  0, 0,  0, 0, -1;
   9,  0,  0,  0, 0,  0, 0,  0, 0;
  10,  0,  0,  0, 0,  0, 0,  0, 0, 0;
  11, 10,  5,  0, 0,  2, 0,  0, 0, 0, 1;

Mathematica

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

Prog

(PARI) T(n, k) = if(k==0, n+1, if(n%k==0, (n/k)*moebius(n), 0));
for(n=0, 10, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Jun 29 2019
(Magma) [[k eq 0 select n+1 else (n mod k) eq 0 select (n/k)*MoebiusMu(n) else 0: k in [0..n]]: n in [0..10]]; // G. C. Greubel, Jun 29 2019

Crossrefs

Sequence in context: A057058 A334441 A278104 * A141671 A309596 A335442

Adjacent sequences: A141669 A141670 A141671 * A141673 A141674 A141675

Keyword

sign,tabl

Author

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

Extensions

Edited by G. C. Greubel, Jun 29 2019

Status

approved