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A140579 Triangle read by rows, A014963(n) * 0^(n-k); 1<=k<=n. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A265494 A091731 A284269 * A132681 A127648 A212209
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson and Mats Granvik, May 17 2008
STATUS
approved

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Last modified March 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)