A388067 Multiplicative sequence a(n) with a(p^e) = (1+floor(e/2)) * (2+floor(e/2)) / 2 for prime p and e >= 0.

1, 1, 1, 3, 1, 1, 1, 3, 3, 1, 1, 3, 1, 1, 1, 6, 1, 3, 1, 3, 1, 1, 1, 3, 3, 1, 3, 3, 1, 1, 1, 6, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 3, 3, 1, 1, 6, 3, 3, 1, 3, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 3, 10, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 3, 3, 1, 1, 1, 6, 6, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 3, 1, 1, 1, 6, 1, 3, 3, 9

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

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

Sum_{k=1..n} a(k) ~ c * n, where c = Pi^4/36 = 2.705808... (A098198). - Amiram Eldar, Sep 16 2025

Mathematica

f[p_, e_] := (1 + Floor[e/2])*(2 + Floor[e/2])/2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 14 2025 *)

Prog

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

Crossrefs

Cf. A098198.

Sequence in context: A180683 A375360 A365331 * A214635 A166030 A351149

Adjacent sequences: A388064 A388065 A388066 * A388068 A388069 A388070

Keyword

nonn,easy,mult

Author

Werner Schulte, Sep 14 2025

Status

approved