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A127481
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Triangle T(n,k) read by rows: T(n,k) = sum_{l=k..n, l|n, k|l} l*phi(k).
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2
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1, 3, 2, 4, 0, 6, 7, 6, 0, 8, 6, 0, 0, 0, 20, 12, 8, 18, 0, 0, 12, 8, 0, 0, 0, 0, 0, 42, 15, 14, 0, 24, 0, 0, 0, 32, 13, 0, 24, 0, 0, 0, 0, 0, 54, 18, 12, 0, 0, 60, 0, 0, 0, 0, 40, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 110, 28, 24, 42, 32, 0, 36, 0, 0, 0, 0, 0, 48, 14, 0, 0, 0, 0, 0, 0, 0, 0
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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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T(n,k) =sum_{l=k..n} A127093(n,l) * A054522(l,k), the matrix product of the infinite lower triangular matrices.
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EXAMPLE
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First few rows of the triangle are:
1;
3, 2;
4, 0, 6;
7, 6, 0, 8;
6, 0, 0, 0, 20,
12, 8, 18, 0, 0, 12;
8, 0, 0, 0, 0, 0, 42;
15, 14, 0, 24, 0, 0, 0, 32;
...
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MAPLE
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a :=0 ;
for l from k to n do
if modp(n, l) =0 and modp(l, k) =0 then
a := a+l*numtheory[phi](k) ;
end if;
end do:
a ;
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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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