A390258 Multiplicative sequence a(n) with a(p^e) = p^(e-1) * (e + 1) * (p * (2 + e) - e) / 2 for prime p and e > 0.

1, 5, 8, 18, 14, 40, 20, 56, 45, 70, 32, 144, 38, 100, 112, 160, 50, 225, 56, 252, 160, 160, 68, 448, 135, 190, 216, 360, 86, 560, 92, 432, 256, 250, 280, 810, 110, 280, 304, 784, 122, 800, 128, 576, 630, 340, 140, 1280, 273, 675, 400, 684, 158, 1080, 448, 1120, 448, 430, 176, 2016

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Formula

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

Dirichlet convolution of A000027 and A018804.

Dirichlet convolution of A038040 and A000010.

Mathematica

f[p_, e_] := p^(e-1) * (e+1) * (p*(e+2) - e)/2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 30 2025 *)

Prog

(PARI) a(n) = { my(f = factor(n)); prod(i=1, #f~, f[i, 1]^(f[i, 2]-1)*(f[i, 2]+1)*(f[i, 1]*(2+f[i, 2])-f[i, 2])/2) }

Crossrefs

Cf. A000010, A000027, A018804, A038040.

Sequence in context: A104321 A196934 A359949 * A291752 A237276 A155086

Adjacent sequences: A390255 A390256 A390257 * A390259 A390260 A390261

Keyword

nonn,easy,mult

Author

Werner Schulte, Oct 30 2025

Status

approved