A370297 Inverse Moebius transform of A322328.

1, 5, 5, 13, 5, 25, 5, 25, 13, 25, 5, 65, 5, 25, 25, 41, 5, 65, 5, 65, 25, 25, 5, 125, 13, 25, 25, 65, 5, 125, 5, 61, 25, 25, 25, 169, 5, 25, 25, 125, 5, 125, 5, 65, 65, 25, 5, 205, 13, 65, 25, 65, 5, 125, 25, 125, 25, 25, 5, 325, 5, 25, 65, 85, 25, 125, 5, 65, 25, 125, 5, 325

Offset

1,2

Links

Table of n, a(n) for n=1..72.

Formula

Multiplicative with a(p^e) = 1 + 2*e*(e+1) for prime p and e >= 0.

Dirichlet g.f.: (zeta(s))^5 / (zeta(2*s))^2.

Dirichlet convolution of A034444 and A048691.

Dirichlet inverse sequence b(n) for n > 0 is multiplicative with b(p) = -5 and b(p^e) = (-1)^e * (8*e-4) for prime p and e > 1.

Mathematica

f[p_, e_] := 2*e^2 + 2*e + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Feb 14 2024 *)

Prog

(PARI) a(n) = factorback(apply(e->1+2*e*(e+1), factor(n)[, 2]))

Crossrefs

Cf. A034444, A048691, A322328.

Sequence in context: A328367 A338085 A302676 * A339947 A206553 A122213

Adjacent sequences: A370294 A370295 A370296 * A370298 A370299 A370300

Keyword

nonn,easy,mult

Author

Werner Schulte, Feb 14 2024

Status

approved