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A054619
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Triangle T(n,k) = Sum_{d|k} phi(d)*n^(k/d).
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6
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1, 2, 6, 3, 12, 33, 4, 20, 72, 280, 5, 30, 135, 660, 3145, 6, 42, 228, 1344, 7800, 46956, 7, 56, 357, 2464, 16835, 118104, 823585, 8, 72, 528, 4176, 32800, 262800, 2097200, 16781472, 9, 90, 747, 6660, 59085, 532350, 4783023, 43053480, 387422001
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OFFSET
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1,2
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LINKS
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EXAMPLE
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1;
2, 6;
3, 12, 33;
4, 20, 72, 280;
5, 30, 135, 660, 3145;
6, 42, 228, 1344, 7800, 46956;
...
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MAPLE
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with(numtheory):
T:= (n, k)-> add(phi(d)*n^(k/d), d=divisors(k)):
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MATHEMATICA
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T[n_, k_] := Sum[EulerPhi[d]*n^(k/d), {d, Divisors[k]}]; Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Feb 25 2015 *)
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PROG
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(PARI) T(n, k) = sumdiv(k, d, eulerphi(d)*n^(k/d)); \\ Michel Marcus, Feb 25 2015
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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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