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A054618 Triangle T(n,k) = Sum_{d|n} phi(d)*k^(n/d). 5
1, 2, 6, 3, 12, 33, 4, 24, 96, 280, 5, 40, 255, 1040, 3145, 6, 84, 780, 4200, 15810, 46956, 7, 140, 2205, 16408, 78155, 279972, 823585, 8, 288, 6672, 65840, 391320, 1681008, 5767328, 16781472, 9, 540, 19755, 262296, 1953405, 10078164, 40354335, 134218800, 387422001 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Rows n = 1..141, flattened

EXAMPLE

1;

2, 6;

3, 12, 33;

4, 24, 96,  280;

5, 40, 255, 1040, 3145;

6, 84, 780, 4200, 15810, 46956;

...

MAPLE

with(numtheory):

T:= (n, k)-> add(phi(d)*k^(n/d), d=divisors(n)):

seq(seq(T(n, k), k=1..n), n=1..10); # Alois P. Heinz, Aug 28 2013

MATHEMATICA

T[n_, k_] := Sum[EulerPhi[d]*k^(n/d), {d, Divisors[n]}]; Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-Fran├žois Alcover, Feb 25 2015 *)

PROG

(PARI) T(n, k) = sumdiv(n, d, eulerphi(d)*k^(n/d)); \\ Michel Marcus, Feb 25 2015

CROSSREFS

Cf. A054619, A054630, A054631.

Main diagonal gives: A228640.

Sequence in context: A092393 A207901 A054619 * A120859 A253258 A098810

Adjacent sequences:  A054615 A054616 A054617 * A054619 A054620 A054621

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Apr 16 2000

STATUS

approved

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Last modified October 13 23:58 EDT 2019. Contains 327986 sequences. (Running on oeis4.)