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A327027 T(n, k) = (1/n) * Sum_{d|n} phi(d) * A241171(n/d, k) for n >= 1, T(0, k) = 0^k. Triangle read by rows for 0 <= k <= n. 2
1, 0, 1, 0, 1, 3, 0, 1, 10, 30, 0, 1, 33, 315, 630, 0, 1, 102, 2646, 15120, 22680, 0, 1, 348, 21135, 263340, 1039500, 1247400, 0, 1, 1170, 167310, 4118400, 32432400, 97297200, 97297200, 0, 1, 4113, 1333080, 61757010, 871620750, 4937832900, 11918907000, 10216206000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

We assume A241171 extended to its (0, 0)-based form.

LINKS

Table of n, a(n) for n=0..44.

EXAMPLE

[0] 1;

[1] 0, 1;

[2] 0, 1, 3;

[3] 0, 1, 10,   30;

[4] 0, 1, 33,   315,    630;

[5] 0, 1, 102,  2646,   15120,   22680;

[6] 0, 1, 348,  21135,  263340,  1039500,  1247400;

[7] 0, 1, 1170, 167310, 4118400, 32432400, 97297200, 97297200;

MAPLE

A327027 := (n, k)-> `if`(n=0, 1, (1/n)*add(phi(d)*A241171(n/d, k), d=divisors(n))):

seq(seq(A327027(n, k), k=0..n), n=0..6);

MATHEMATICA

A327027[0,  k_] := 1;

A327027[n_, k_] := DivisorSum[n, EulerPhi[#] A241171[n/#, k] &] / n;

Table[A327027[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

PROG

(Sage) # uses[DivisorTriangle from A327029, A241171]

DivisorTriangle(euler_phi, A241171, 8, lambda n: 1/n if n > 1 else 1)

CROSSREFS

Cf. A327021 (main diagonal), A327026 (row sums), A241171, A327029.

Sequence in context: A307657 A269939 A239731 * A145881 A232223 A245111

Adjacent sequences:  A327024 A327025 A327026 * A327028 A327029 A327030

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Aug 20 2019

STATUS

approved

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Last modified January 25 09:50 EST 2022. Contains 350565 sequences. (Running on oeis4.)