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

1,2

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, Composito Mathem. 151 (6) (2015), 999-1040, E_{k+2,psi,tau).

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

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 *)

Crossrefs

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

Sequence in context: A058532 A370107 A280966 * A174466 A070422 A102574

Adjacent sequences: A360427 A360428 A360429 * A360431 A360432 A360433

Keyword

nonn,mult,easy

Author

R. J. Mathar, Feb 07 2023

Status

approved