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

1,3

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

Formula

A126988 as an infinite lower triangular matrix, * A000594.

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 *)

Prog

(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

Crossrefs

Cf. A126988, A000594, A128378, A128379, A128380, A128381, A128391.

Sequence in context: A237369 A280936 A250871 * A296784 A235078 A235072

Adjacent sequences: A128389 A128390 A128391 * A128393 A128394 A128395

Keyword

sign,mult

Author

Gary W. Adamson, Feb 28 2007

Extensions

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

Status

approved