A359949 Multiplicative sequence with a(p) = 3*p-1 and a(p^e) = (3*e*(p-1) + 3) * p^(e-1) for e > 1 and prime p.

1, 5, 8, 18, 14, 40, 20, 48, 45, 70, 32, 144, 38, 100, 112, 120, 50, 225, 56, 252, 160, 160, 68, 384, 135, 190, 189, 360, 86, 560, 92, 288, 256, 250, 280, 810, 110, 280, 304, 672, 122, 800, 128, 576, 630, 340, 140, 960, 273, 675, 400, 684, 158, 945, 448, 960, 448, 430, 176, 2016

Offset

1,2

Links

Table of n, a(n) for n=1..60.

Formula

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

Dirichlet convolution of A000010(n) and n * A073184(n).

a(n) = Sum_{k=1..n} gcd(k, n) * A073184(gcd(k, n)).

Mathematica

f[p_, e_] := If[e == 1, 3*p - 1, (3*e*(p - 1) + 3)*p^(e - 1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 19 2023 *)

Prog

(PARI) a(n) = my(f=factor(n), p, e); for (k=1, #f~, p=f[k, 1]; e=f[k, 2]; f[k, 1] = if (e == 1, 3*p-1, (3*e*(p-1) + 3) * p^(e-1)); f[k, 2] = 1); factorback(f); \\ Michel Marcus, Jan 21 2023

Crossrefs

Cf. A000010, A073184.

Sequence in context: A280251 A104321 A196934 * A291752 A237276 A155086

Adjacent sequences: A359946 A359947 A359948 * A359950 A359951 A359952

Keyword

nonn,easy,mult

Author

Werner Schulte, Jan 19 2023

Status

approved