A373039 a(n) = (A372966(n) - 1)/240.

0, 1, 27, 257, 1625, 6508, 24010, 65793, 177174, 391626, 893101, 1665644, 3398759, 5786411, 10531652, 16843009, 29065308, 42698935, 70764303, 100231882, 155608837, 215237342, 326294606, 426404460, 634767250, 819100920, 1162438641, 1480961067, 2084357107, 2538128133

Offset

1,3

Links

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

Formula

From Amiram Eldar, Jan 08 2025: (Start)

Dirichlet g.f.: zeta(s) * (zeta(s-8)/zeta(s-4) - 1)/240.

Sum_{k=1..n} a(k) ~ c * n^9, where c = zeta(9)/(2160*zeta(5)) = 0.000447372... . (End)

Mathematica

f[p_, e_] := (p^(8*e + 4) + 1)/(p^4 + 1); a[1] = 0; a[n_] := (Times @@ f @@@ FactorInteger[n] - 1) / 240; Array[a, 30] (* Amiram Eldar, Jan 08 2025 *)

Prog

(PARI) a(n) = (sigma(n^2, 8)/sigma(n^2, 4)-1)/240

Crossrefs

Cf. A000290, A001159, A013956.

Sequence in context: A374894 A132652 A349507 * A125390 A126548 A108670

Adjacent sequences: A373036 A373037 A373038 * A373040 A373041 A373042

Keyword

nonn,changed

Author

Hugo Pfoertner, May 20 2024

Status

approved