%I #20 Jan 21 2020 11:58:43
%S 1,2,6,3,12,33,4,20,72,280,5,30,135,660,3145,6,42,228,1344,7800,46956,
%T 7,56,357,2464,16835,118104,823585,8,72,528,4176,32800,262800,2097200,
%U 16781472,9,90,747,6660,59085,532350,4783023,43053480,387422001
%N Triangle T(n,k) = Sum_{d|k} phi(d)*n^(k/d).
%H Alois P. Heinz, <a href="/A054619/b054619.txt">Rows n = 1..141, flattened</a>
%e 1;
%e 2, 6;
%e 3, 12, 33;
%e 4, 20, 72, 280;
%e 5, 30, 135, 660, 3145;
%e 6, 42, 228, 1344, 7800, 46956;
%e ...
%p with(numtheory):
%p T:= (n, k)-> add(phi(d)*n^(k/d), d=divisors(k)):
%p seq(seq(T(n,k), k=1..n), n=1..10); # _Alois P. Heinz_, Aug 28 2013
%t 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 *)
%o (PARI) T(n, k) = sumdiv(k, d, eulerphi(d)*n^(k/d)); \\ _Michel Marcus_, Feb 25 2015
%Y Cf. A054618, A054630, A054631, A185651 (transpose).
%Y Main diagonal gives: A228640.
%K nonn,tabl
%O 1,2
%A _N. J. A. Sloane_, Apr 16 2000
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