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A127173
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T(n,k) = A007427(n/k) if k divides n, T(n,k) = 0 otherwise.
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1
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1, -2, 1, -2, 0, 1, 1, -2, 0, 1, -2, 0, 0, 0, 1, 4, -2, -2, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, -2, 0, 0, 0, 1, 1, 0, -2, 0, 0, 0, 0, 0, 1, 4, -2, 0, 0, -2, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 4, 1, -2, 0, -2, 0, 0, 0, 0, 0, 1
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OFFSET
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1,2
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LINKS
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FORMULA
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Square of A054525 as lower triangular matrix.
A007431(n) = Sum_{k=1, n} k*T(n,k).
A007428(n) = Sum_{k=1..n} mu(k)*T(n,k).
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EXAMPLE
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First few rows of the triangle:
1;
-2, 1;
-2, 0, 1;
1, -2, 0, 1;
-2, 0, 0, 0, 1;
4, -2, -2, 0, 0, 1;
-2, 0, 0, 0, 0, 0, 1;
0, 1, 0, -2, 0, 0, 0, 1;
1, 0, -2, 0, 0, 0, 0, 0, 1;
4, -2, 0, 0, -2, 0, 0, 0, 0, 1;
...
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PROG
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b(n)={sumdiv(n, d, moebius(d) * moebius(n/d))}
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Missing a(10)-a(14) and a(56) and beyond from Andrew Howroyd, Feb 20 2022
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STATUS
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approved
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