A128392 A126988^12 * A000594.

1, 0, 288, -1736, 4890, 0, -16660, 44576, -103869, 0, 534744, -499968, -577582, 0, 1408320, 2507344, -6905730, 0, 10661648, -8489040, -4798080, 0, 18643548, 12837888, -25207475, 0, -77183496, 28921760, 128406978, 0, -52842796, -151328128, 154006272, 0, -81467400

Offset: 1

Author

Gary W. Adamson, Feb 28 2007

Keywords

• sign
• mult

Comments

Conjecture: Given A126988^k, k any positive integer, A128392 is the only sequence in the infinite set with zeros.

Each application of A126988 corresponds to the Dirichlet convolution of the natural numbers with the sequence on the right. Since both Ramanujan's tau function A000594 and the natural numbers 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. A126988, A000594, A128378, A128379, A128380, A128381, A128391.

Programs

Mathematica

nmax = 40;
M = Table[If[Mod[n, m] == 0, n/m, 0], {n, 1, nmax}, {m, 1, nmax}];
MatrixPower[M, 12].RamanujanTau[Range[nmax]] (* Jean-François Alcover, Sep 20 2019 *)

PARI

seq(n, k=12)={my(u=vector(n,n,n), v=vector(n,n,ramanujantau(n))); for(i=1, k, v=dirmul(u,v)); v} \\ Andrew Howroyd, Aug 03 2018

Formula

A126988 as an infinite lower triangular matrix, * A000594.

Extensions

Terms a(11) and beyond from Andrew Howroyd, Aug 03 2018