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A360430 Dirichlet convolution of Dedekind psi by A038040.

%I A360430 #15 Mar 25 2025 02:31:03
%S A360430 1,7,10,30,16,70,22,104,63,112,34,300,40,154,160,320,52,441,58,480,
%T A360430 220,238,70,1040,165,280,324,660,88,1120,94,912,340,364,352,1890,112,
%U A360430 406,400,1664,124,1540,130,1020,1008,490,142,3200,315,1155
%N A360430 Dirichlet convolution of Dedekind psi by A038040.
%H A360430 Amiram Eldar, <a href="/A360430/b360430.txt">Table of n, a(n) for n = 1..10000</a>
%H A360430 Joël Bellaïche and Samit Dasgupta, <a href="https://dx.doi.org/10.1112/S0010437X1400788X">The p-adic L-functions of evil Eisenstein series</a>, Compositio Mathem. 151 (6) (2015), 999-1040, E_{k+2,psi,tau}.
%F A360430 a(n) = Sum_{d|n} A001615(n/d)*A000005(d)*d.
%F A360430 Dirichlet g.f.: zeta(s-1)^3*zeta(s)/zeta(2*s).
%F A360430 Dirichlet convolution of A008966 by A034718.
%F A360430 Multiplicative with a(p^e) = ((e+2)*p + e)*(e+1)*p^(e-1)/2. - _Amiram Eldar_, Feb 09 2023
%p A360430 A360430 := proc(n)
%p A360430     add(A001615(n/d)*numtheory[tau](d)*d,d=numtheory[divisors](n)) ;
%p A360430 end proc:
%t A360430 f[p_, e_] := ((e+2)*p + e)*(e+1)*p^(e-1)/2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Feb 09 2023 *)
%Y A360430 Cf. A000005, A001615, A008966, A034718, A038040, A060724.
%K A360430 nonn,mult,easy
%O A360430 1,2
%A A360430 _R. J. Mathar_, Feb 07 2023