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

1,3

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

Formula

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A054026 A237773 A188252 * A328132 A234412 A234406

Adjacent sequences: A128388 A128389 A128390 * A128392 A128393 A128394

Keyword

sign,mult

Author

Gary W. Adamson, Feb 28 2007

Extensions

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

Status

approved