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A341305 Fourier coefficients of the modular form (1/28)*(E_6(t)+27*E_6(3*t)).

%I A341305 #17 Apr 30 2023 11:19:18
%S A341305 1,-18,-594,-4878,-19026,-56268,-160974,-302544,-608850,-1185858,
%T A341305 -1856844,-2898936,-5156046,-6683292,-9983952,-15248628,-19483218,
%U A341305 -25557444,-39133314,-44569800,-59475276,-81989424,-95664888,-115854192,-164998350,-175837518,-220548636,-288163998,-319789008,-369200700
%N A341305 Fourier coefficients of the modular form (1/28)*(E_6(t)+27*E_6(3*t)).
%H A341305 Masao Koike, <a href="https://oeis.org/A004016/a004016.pdf">Modular forms on non-compact arithmetic triangle groups</a>, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021. I wrote 2005 on the first page but the internal evidence suggests 1997.] See page 29.
%p A341305 A341305 := proc(n)
%p A341305     local a;
%p A341305     a := A013973(n);
%p A341305     if modp(n,3) = 0 then
%p A341305         a := a+27*A013973(n/3) ;
%p A341305     end if;
%p A341305     %/28 ;
%p A341305 end proc:
%p A341305 seq(A341305(n),n=0..10) ; # _R. J. Mathar_, Feb 22 2021
%t A341305 A013973[n_] := If[n == 0, 1, -504 DivisorSigma[5, n]];
%t A341305 A341305[n_] := Module[{a = A013973[n]}, If[Mod[n, 3] == 0, a = a + 27 A013973[n/3]]; a/28];
%t A341305 Table[A341305[n], {n, 0, 29}] (* _Jean-François Alcover_, Apr 30 2023, after _R. J. Mathar_ *)
%Y A341305 Cf. A013973.
%K A341305 sign
%O A341305 0,2
%A A341305 _N. J. A. Sloane_, Feb 13 2021