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

1,3

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

Links

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

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.

Example

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;
...

Mathematica

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

Prog

(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

Crossrefs

Cf. A014963, A140580, A048671.

Cf. A008683, A140664.

Sequence in context: A265494 A091731 A284269 * A132681 A127648 A212209

Adjacent sequences: A140576 A140577 A140578 * A140580 A140581 A140582

Keyword

nonn,tabl

Author

Gary W. Adamson and Mats Granvik, May 17 2008

Status

approved