A141672 - OEIS

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

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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:

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