cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A128391 A054523^24 * A000594.

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%I A128391 #9 Sep 20 2019 08:05:40
%S A128391 1,0,300,-1724,4926,0,-16600,44600,-100299,0,534852,-517200,-577450,0,
%T A128391 1477800,2486626,-6905550,0,10661852,-8492424,-4980000,0,18643800,
%U A128391 13380000,-25030649,0,-78396200,28618400,128407302,0,-52842448,-150834520,160455600,0,-81771600
%N A128391 A054523^24 * A000594.
%C A128391 Conjecture: Given A054523^k, k = any positive integer, "zero" appears only in the sequence A018391 (k=24).
%C A128391 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
%H A128391 Andrew Howroyd, <a href="/A128391/b128391.txt">Table of n, a(n) for n = 1..1000</a>
%F A128391 A054523^24 as an infinite lower triangular matrix * A000594.
%t A128391 nmax = 40;
%t A128391 T[n_, k_] := If[Divisible[n, k], EulerPhi[n/k], 0]; T[1, 1] = 1;
%t A128391 M = Table[T[n, k], {n, 1, nmax}, {k, 1, nmax}];
%t A128391 MatrixPower[M, 24].RamanujanTau[Range[nmax]] (* _Jean-François Alcover_, Sep 20 2019 *)
%o A128391 (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
%Y A128391 Cf. A000010, A000594, A054523, A128378, A128379, A128380, A128381, A128392.
%K A128391 sign,mult
%O A128391 1,3
%A A128391 _Gary W. Adamson_, Feb 28 2007
%E A128391 a(7) corrected and terms a(11) and beyond from _Andrew Howroyd_, Aug 03 2018