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A140579
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Triangle read by rows, A014963(n) * 0^(n-k); 1<=k<=n.
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7
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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
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OFFSET
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1,3
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COMMENTS
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(A140579)^(-1) * [1, 2, 3,...] = A048671: (1, 1, 1, 2, 1, 6, 1, 4, 3, 10,...).
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LINKS
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FORMULA
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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.
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EXAMPLE
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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;
...
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MATHEMATICA
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Table[If[k != n , 0, Exp[MangoldtLambda[n]]], {n, 1, 12}, {k, 1, n}]//Flatten (* G. C. Greubel, Feb 16 2019 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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