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A054619 Triangle T(n,k) = Sum_{d|k} phi(d)*n^(k/d). 6

%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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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)