A360430 Dirichlet convolution of Dedekind psi by A038040.

1, 7, 10, 30, 16, 70, 22, 104, 63, 112, 34, 300, 40, 154, 160, 320, 52, 441, 58, 480, 220, 238, 70, 1040, 165, 280, 324, 660, 88, 1120, 94, 912, 340, 364, 352, 1890, 112, 406, 400, 1664, 124, 1540, 130, 1020, 1008, 490, 142, 3200, 315, 1155

Offset: 1

Author

R. J. Mathar, Feb 07 2023

Keywords

• nonn
• mult
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Joël Bellaïche and Samit Dasgupta, The p-adic L-functions of evil Eisenstein series, Compositio Mathem. 151 (6) (2015), 999-1040, E_{k+2,psi,tau}.

Crossrefs

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

Programs

Maple

A360430 := proc(n)
    add(A001615(n/d)*numtheory[tau](d)*d,d=numtheory[divisors](n)) ;
end proc:

Mathematica

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 *)

Formula

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

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

Dirichlet convolution of A008966 by A034718.

Multiplicative with a(p^e) = ((e+2)*p + e)*(e+1)*p^(e-1)/2. - Amiram Eldar, Feb 09 2023