A140579 Triangle read by rows, A014963(n) * 0^(n-k); 1<=k<=n.

1, 0, 2, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13

Offset: 1

Author

Gary W. Adamson and Mats Granvik, May 17 2008

Keywords

• nonn
• tabl

Comments

A140579 * [1, 2, 3,...] = A140580.

(A140579)^(-1) * [1, 2, 3,...] = A048671: (1, 1, 1, 2, 1, 6, 1, 4, 3, 10,...).

A008683 = A140579^(-1) * A140664. - Gary W. Adamson, May 20 2008

Examples

			First few rows of the triangle are:
1;
0, 2;
0, 0, 3;
0, 0, 0, 2;
0, 0, 0, 0, 5;
0, 0, 0, 0, 0, 1;
0, 0, 0, 0, 0, 0, 7;
...
		

Links

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

Crossrefs

Cf. A014963, A140580, A048671.

Cf. A008683, A140664.

Programs

Mathematica

Table[If[k != n ,0,Exp[MangoldtLambda[n]]], {n,1,12}, {k,1,n}]//Flatten (* G. C. Greubel, Feb 16 2019 *)

PARI

{T(n,k) = if(n==1, 1, gcd(vector(n-1, k, binomial(n, k)))*0^(n-k))};
for(n=1,12, for(k=1,n, print1(T(n,k), ", "))) \\ G. C. Greubel, Feb 16 2019

Sage

def T(n,k): return simplify(exp(add(moebius(d)*log(n/d) for d in divisors(n))))*0^(n-k)
[[T(n,k) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Feb 16 2019

Formula

Triangle read by rows, A014963(n) * 0^(n-k); 1<=k<=n.

Infinite lower triangular matrix with A014963 (1, 2, 3, 2, 5, 1, 7, 2, 3, 1, 11,...) in the main diagonal and the rest zeros.