A370240 The sum of divisors of n that are cubes of squarefree numbers.

1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 28, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 28, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 28, 1, 1, 1, 1, 1

Offset

1,8

Comments

First differs from A366904 at n = 32, and from A113061 at n = 64.

Links

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

Formula

Multiplicative with a(p^e) = 1 for e <= 2, and a(p^e) = 1 + p^3 for e >= 3.

Dirichlet g.f.: zeta(s)*zeta(3*s-3)/zeta(6*s-6).

Sum_{k=1..n} a(k) ~ c * n^(4/3) + n, where c = 3*zeta(4/3)/(2*Pi^2) = 0.5472769126... .

Mathematica

f[p_, e_] := If[e <= 2, 1, 1 + p^3]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] <= 2, 1, 1 + f[i, 1]^3)); }

Crossrefs

Cf. A062838, A113061, A366904, A370239.

Sequence in context: A078297 A189788 A264981 * A113061 A366904 A284099

Adjacent sequences: A370237 A370238 A370239 * A370241 A370242 A370243

Keyword

nonn,easy,mult

Author

Amiram Eldar, Feb 13 2024

Status

approved