A128391 A054523^24 * A000594.

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

Author

Gary W. Adamson, Feb 28 2007

Keywords

• sign
• mult

Comments

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

Links

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

Crossrefs

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

Programs

Mathematica

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 *)

PARI

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

Formula

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

Extensions

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