A360430 - OEIS

%I #15 Mar 25 2025 02:31:03

%S 1,7,10,30,16,70,22,104,63,112,34,300,40,154,160,320,52,441,58,480,

%T 220,238,70,1040,165,280,324,660,88,1120,94,912,340,364,352,1890,112,

%U 406,400,1664,124,1540,130,1020,1008,490,142,3200,315,1155

%N Dirichlet convolution of Dedekind psi by A038040.

%H Amiram Eldar, <a href="/A360430/b360430.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 a(n) = Sum_{d|n} A001615(n/d)*A000005(d)*d.

%F Dirichlet g.f.: zeta(s-1)^3*zeta(s)/zeta(2*s).

%F Dirichlet convolution of A008966 by A034718.

%F Multiplicative with a(p^e) = ((e+2)*p + e)*(e+1)*p^(e-1)/2. - _Amiram Eldar_, Feb 09 2023

%p A360430 := proc(n)

%p     add(A001615(n/d)*numtheory[tau](d)*d,d=numtheory[divisors](n)) ;

%p end proc:

%t 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 Cf. A000005, A001615, A008966, A034718, A038040, A060724.

%K nonn,mult,easy

%O 1,2

%A _R. J. Mathar_, Feb 07 2023