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A247343 Moebius transform applied four times to sequence 1,0,0,0,....

%I A247343 #27 Feb 22 2021 04:09:11
%S A247343 1,-4,-4,6,-4,16,-4,-4,6,16,-4,-24,-4,16,16,1,-4,-24,-4,-24,16,16,-4,
%T A247343 16,6,16,-4,-24,-4,-64,-4,0,16,16,16,36,-4,16,16,16,-4,-64,-4,-24,-24,
%U A247343 16,-4,-4,6,-24,16,-24,-4,16,16,16,16,16,-4,96,-4,16,-24,0,16,-64,-4,-24,16,-64
%N A247343 Moebius transform applied four times to sequence 1,0,0,0,....
%C A247343 Multiplicative because the Moebius transform of a multiplicative sequence is multiplicative. - _Andrew Howroyd_, Jul 25 2018
%H A247343 Amiram Eldar, <a href="/A247343/b247343.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5000 from Enrique Pérez Herrero)
%F A247343 Dirichlet g.f.: 1/zeta(s)^4.
%F A247343 Multiplicative with a(p^e) = (-1)^e * binomial(4, e). - _Amiram Eldar_, Sep 11 2020
%t A247343 tau[1, n_Integer]:=1; SetAttributes[tau, Listable];
%t A247343 tau[k_Integer, n_Integer]:=Plus@@(tau[k-1, Divisors[n]])/; k > 1;
%t A247343 tau[k_Integer, n_Integer]:=Plus@@(tau[k+1, Divisors[n]]*MoebiusMu[n/Divisors[n]]); k<1;
%t A247343 Table[tau[-4, n], {n, 70}]
%t A247343 f[p_, e_] := (-1)^e * Binomial[4, e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Sep 11 2020 *)
%o A247343 (PARI) seq(n)={my(v=vector(n, n, n==1)); for(k=1, 4, v=dirmul(v, vector(#v, n, moebius(n)))); v} \\ _Andrew Howroyd_, Jul 25 2018
%o A247343 (PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - X)^4)[n], ", ")) \\ _Vaclav Kotesovec_, Feb 22 2021
%Y A247343 Cf. A000007, A008683, A007427, A007428.
%K A247343 sign,mult,easy
%O A247343 1,2
%A A247343 _Enrique Pérez Herrero_, Sep 14 2014