|
%I #9 Sep 20 2019 08:08:37
%S 1,0,288,-1736,4890,0,-16660,44576,-103869,0,534744,-499968,-577582,0,
%T 1408320,2507344,-6905730,0,10661648,-8489040,-4798080,0,18643548,
%U 12837888,-25207475,0,-77183496,28921760,128406978,0,-52842796,-151328128,154006272,0,-81467400
%N A126988^12 * A000594.
%C Conjecture: Given A126988^k, k any positive integer, A128392 is the only sequence in the infinite set with zeros.
%C 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
%H Andrew Howroyd, <a href="/A128392/b128392.txt">Table of n, a(n) for n = 1..1000</a>
%F A126988 as an infinite lower triangular matrix, * A000594.
%t nmax = 40;
%t M = Table[If[Mod[n, m] == 0, n/m, 0], {n, 1, nmax}, {m, 1, nmax}];
%t MatrixPower[M, 12].RamanujanTau[Range[nmax]] (* _Jean-François Alcover_, Sep 20 2019 *)
%o (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
%Y Cf. A126988, A000594, A128378, A128379, A128380, A128381, A128391.
%K sign,mult
%O 1,3
%A _Gary W. Adamson_, Feb 28 2007
%E Terms a(11) and beyond from _Andrew Howroyd_, Aug 03 2018
|
