A128392 -id:A128392 - cp's OEIS frontend

1, 0, 300, -1724, 4926, 0, -16600, 44600, -100299, 0, 534852, -517200, -577450, 0, 1477800, 2486626, -6905550, 0, 10661852, -8492424, -4980000, 0, 18643800, 13380000, -25030649, 0, -78396200, 28618400, 128407302, 0, -52842448, -150834520, 160455600, 0, -81771600

Offset: 1

Gary W. Adamson, Feb 28 2007

Conjecture: Given A054523^k, k = any positive integer, "zero" appears only in the sequence A018391 (k=24).

Each application of A054523 corresponds to the Dirichlet convolution of A000010 with the sequence on the right. Since both A000594 and A000010 are multiplicative, the resulting sequence will also be multiplicative. - Andrew Howroyd, Aug 03 2018

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Cf. A000010, A000594, A054523, A128378, A128379, A128380, A128381, A128392.

nmax = 40;
T[n_, k_] := If[Divisible[n, k], EulerPhi[n/k], 0]; T[1, 1] = 1;
M = Table[T[n, k], {n, 1, nmax}, {k, 1, nmax}];
MatrixPower[M, 24].RamanujanTau[Range[nmax]] (* Jean-François Alcover, Sep 20 2019 *)

seq(n, k=24)={my(u=vector(n,n,eulerphi(n)), v=vector(n,n,ramanujantau(n))); for(i=1, k, v=dirmul(u,v)); v} \\ Andrew Howroyd, Aug 03 2018

A054523^24 as an infinite lower triangular matrix * A000594.

a(7) corrected and terms a(11) and beyond from Andrew Howroyd, Aug 03 2018

cp's OEIS Frontend

A128391 A054523^24 * A000594.

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